How To Find Product Key In Windows 10 In Lenovo Laptop

It is very good to access a locked hard drive that was locked by a BIOS supervisor password, it is very good to have such a handy windows GUI interface to recover some files. The iBios software can brick your BIOS and is badly done. There is one handy software, NTPWEdit, that is based on Windows GUI that can reset your passwords for the Admin and other users of the Windows OS and It did work nicely for me, it's simple to use. There is probably some good software in the package like Imgburn and other well known programs however there is also a lot of badly made software. I would give this bunch of software pack a vote of 6. It does not pass the real test quality necessary for a computer expert.

There are a few ways to retrieve a key from an unbootable computer and most of them involve having access to another working computer. For example, taking out the hard drive and attaching it to a working machine, running a tool that can read product keys, load the registry hive from within the program and retrieve the product key. Or you can boot up PCRegedit, load the registry and then decrypt the key from a working computer. All those steps work but are a bit fiddly and time consuming. If the user has to reinstall the operating system on a computer with Windows 8, the installation process automatically captures key software product of the motherboard BIOS without input from the user.

This means that these stickers familiar windows product key will no longer appear on Windows 8 computers. If you're a computer technician or the neighborhood tech geek, quite frequently you could find yourself having to reinstall Windows for people. With the launch of Windows 10, product keys have become less important because Microsoft launched digital licenses in 2016. Digital licenses allow for the simple installation of an operating system without requiring a bootable device. The operating system can be activated via your Microsoft account. Even when you're reinstalling Windows 10, the system detects the license automatically.

One reader told us that, according to HP, it does not put product key on laptops or PCs for security reasons. As with the Digital Entitlement or Digital Licence, the product key is stored 'somewhere in the computer' and will activate automatically if needed. This is supposed to work even if the hard drive fails.

If your hp laptop comes with preinstalled and preactivated windows 10 that means your product key is stored in BIOS. When you upgrade to Windows 10 from Windows 7 or Windows 8.1, or to Windows 11 from Windows 10, a digital license activates the copy of Windows instead of a product key. These digital keys are linked to your Microsoft Account. So after reinstalling Windows, sign in with the same account.

I want to reinstall Windows XP on my Dell computer. I have the oem disc, but it is mixed with the other two provided with two other computers Dell oem disks that were purchased at the same time. The sticker on my computer displays a product key. When I do a search for product key on the computer using a program key finder, sometimes with a different product key. Which should I use and is at - there a way to find the product key on the disc? The Helix is a convertible laptop satisfying both tablet and conventional notebook users.

It uses a "rip and flip" design that allows the user to detach the display and then replace it facing in a different direction. In 2020, Lenovo shifted into much heavier support of Linux when they announced the ThinkPad X1 Carbon Gen 8, the P1 Gen 2, and the P53 would come with Fedora Linux as an option. This was the first time that Fedora Linux was made available as a preinstalled option from a major hardware vendor. Following that, Lenovo then began making Ubuntu available as a preinstalled option across nearly thirty different notebook and desktop models, and Fedora Linux on all of its P series lineup. For Windows XP, Windows 7 or windows vista users, click on the start-up menu.

Just above it, there is a search bar on the search bar type in cmd for command prompt. An option of exe appears in the start-up menu. As I've said, Windows OS is now downloadable. Therefore, long gone are the days of printed installation keys. But what happens if your hard disc needs formatting due to malware or virus attack? Or, you want to reinstall the operative system?

These are some of the reasons why it's a bright idea to find the Windows 7 product key. Remember, Microsoft no longer supports Windows 7. Therefore, it's best to switch to Windows 10 or 8 to enjoy frequent updates. Before downloads became common, Windows operating systems came in physical optical discs like CDs. But due to duplication issues, Microsoft began assigning specific numbers to each copy sold. This way, the software can only be used after entering the included installation key.

So, Windows 7 license or product key is a 25-character code that activates the operating system after installing it.This key is sometimes called a product code, CD key, or key code. After activating a Windows 7 computer, it will be foolhardy to think that you won't need the activation key anymore. Let's say you want to reinstall the operating system, but you've misplaced or forgot the key. While this may sound intimidating at first, learning how to find Windows 7 product keyis straightforward with the right methods.

So, read on to learnhow to find Windows 7 product key using CMDand other simple recovery methods. In case you lose this number, you can use third-party softwares like ProduKey to find it on an existing installation. I downloaded that tiny tool from NeoSmart and it worked instantly with zero thinking or button pressing. I don't know what edition of Windows10 this laptop came with, other that it's a Windows 10 Dell Edition of Windows. Dell Support lets me download a recovery multi-OS image for a flashdrive but it doesn't say what OS this PC shipped with.

I don't think Microsoft ever made a special series of keys just for Dell, so this key must be for either Home or Pro. Is there some way to know what OS this key is for? I tried entering it into my laptop and it simply said it's not the right version of Windows. How do you know it got its product key from BIOS? You should confirm your laptop has a BIOS key with produkey or another key recovery tool. You should be creating the installation media with the "media creation tool" and making sure to choose the same version and language of Windows (home / pro) as what the laptop came with during install.

Windows 10 typically pulls the key automatically during install and doesn't even ask what version to install nor does it ask for a key. So these are the five ways you can use to find the Windows 11 product key on your PC. For me, running the command on the CMD window worked like a charm. If that didn't work for you, the third-party tool is an excellent alternative. Not to mention, you still have the VBS script that displays your license key instantly.

If you want to learn the difference between Windows 11 Home and Pro, go through our in-depth comparison. And to legally buy a Windows license key at a lower cost, head over to our linked article. And if you have any questions, let us know in the comment section below. While Windows 11 comes as a free upgrade for Windows 10 users, users still want to find the product key in case they lose activation after moving to Windows 11. So to make it easier for you, we have compiled this handy guide on how to find your Windows 11 product key in a jiffy.

No matter if you have a digital license linked to your Microsoft account or an OEM license tied to your laptop, you can easily find the product key on Windows 11. So without any delay, let's check out the different methods. These days Windows 10 is the OS that comes preinstalled on most devices by the manufacturer itself. But the problem arises when you need to reinstall Windows. You must enter the key to activate Windows, and these days, the manufacturers don't offer any documentation for that.

In specific, we observed that many Lenovo users are having issues activating Windows after a reinstall, so today, we will help them troubleshoot these issues. However, it lacked the lid latch mechanism which was present on the previous X200 and X201 versions. I just wanted to let everyone know this is relevant to Windows 10. Windows 10 would partially boot and then just hang, I'm assuming upon loading the graphics card. Some may find the above two Windows 7 product ID recovery methods complicated to understand or can't find the product key altogether.

Instead, use the PassFab Product Key Recovery. It's a lightweight, fast, and simple-to-use desktop program that allows you to find Windows 7 registration key with a single mouse click. On top of Windows 7, users can also recover license keys for Windows 10, 8, XP, and Vista. Surprisingly, it can recover activation IDs for Internet Explorer, SQL Server, and Microsoft Office 2019,2016, 2013, 2010, and 2007. If you need to find the product key for your Windows 10 installation, you've got a few options. The key can be retrieved via the BIOS i.e. the bootloader of your system or the command window.

You can also use external software to retrieve your Windows 10 key. Since Microsoft has your computer's 'digital signature' from the initial upgrade it recognises the combination of components when you do a clean install and automatically activates Windows. This means you can safely skip the screen which asks for a product key at the start of the installation process.

This will reveal the partial product key which gives an idea of the product key that is in use. Compare with product keys that you have and it will confirm copy of which is in use. When we're done, click OK and close the command prompt window.

For example, if you bought 3 copies of Windows 7 Professional, installed one, active, but later wanted to update another PC but can't remember which key was used, this trick can be very handy. However, before you can clean install a copy of Windows 10, you will need to upgrade your current Windows 8.1 installation to Windows 10 then activate it. This step will convert your Windows 8.1 key to a Windows 10 key and syncs your hardware ID and activation license to the Microsoft servers. Once you have an activated copy of Windows 10, you can clean install and activate Windows 10. The ThinkPad Yoga is an Ultrabook-class convertible device that functions as both a laptop and tablet computer.

The Yoga gets its name from the consumer-oriented IdeaPad Yoga line of computers with the same form factor. The ThinkPad Yoga has a backlit keyboard that flattens when flipped into tablet mode. On later X1 Yoga generations, the keys themselves retract in the chassis, so the computer rests on fixed small pads. Lenovo implemented this design in response to complaints about its earlier Yoga 13 and 11 models being awkward to use in tablet mode. A reinforced hinge was required to implement this design. Other than its convertible form factor, the ThinkPad Yoga retains standard ThinkPad features such as a black magnesium-reinforced chassis, island keyboard, a red TrackPoint, and a large touchpad.

The first tool to try and recover your Windows product key is Lazesoft Recover My Password Home Edition. It's also about as easy to use as you could expect this type of recovery task to get. I'm confident you can now find the Windows 7 product key using CMDeffortlessly. While it beats logic why Microsoft makes it a bit complicated to locate the product keys, we can assume that the company doesn't want any third-party access.

Nonetheless, using the command prompt offers super-fast results. But if you intend to locate the installation key for Windows 10, 8, or 7, use Registry or PassFab Product Key Finder. Just install and run it, and recover your product key.

It's vital to remember that the product key comes in the Windows 7 OS card inside the box. If your computer comes preinstalled with Windows, the product key should be on the COA sticker on the device. And if you can't find or lost the key, contact the manufacturer or apply some quick fixes to get Windows 7 product key using Command prompt, Registry or Product key finder. A product key is usually subdivided into multiple parts comprised of a combination of various letters and numbers. Each licensing key is unique and can only be used with a single version of a purchased software.

Through a special procedure, the licensing key is tested for its authenticity. The first ever licensing key was used as part of the Windows 95 operating system and was displayed on the installation disc cover. Windows justified the issue of a licensing code by saying that it was trying to avoid illegal usage of its licensed software. To check, you'll need to look for a certificate of authenticity sticker on your computer.

The COA sticker verifies that the computer came with an authentic copy of Windows, and that sticker has a product key printed on it. You'll need that product key to reinstall Windows–and, if the manufacturer used System Locked Pre-installation, that key is different from the one your PC came with in software. This digital license serves all the same purposes as the product key. Even better, it's built into the OS — this means that if you need to reinstall or upgrade Windows, you won't need to enter it. Whenever we first activate the Windows operating system with the product key, it is saved in the bios of your system.

So we can easily find it by using some command prompt commands or any third-party key finder tool. If you have a Windows laptop, the license sticker is generally glued to the underside of the computer. Just turn back your laptop and look for a 25-character product key. Keep in mind, if you bought the laptop running Windows 10 or 7, the license key will still work without any issues on your upgraded Windows 11 PC.

However, if you are building a custom PC, you will have to buy the retail product key for Windows. Keep in mind that you can keep using this retail key as you upgrade your hardware over time. On the other hand, the product key that comes with Windows laptops is tied to its motherboard and can only be used on that particular laptop. These product keys are called OEM license keys. So that's a brief explainer on what is a product key for Windows. If you have not formatted windows, download and run belarc advisor.

Where Is My Windows 10 Product Key Lenovo Laptop With Windows 8, Microsoft changed stickers that have the product key that the user must type in during the installation of the operating system of new embedded BIOS product key. The idea is that by eliminating the tile, you eliminate one of the easiest ways for nefarious users get a legitimate product key. Since the Windows 8 launch, the OEM's stores and encrypts the product key of Windows in the UEFI or BIOS firmware chip. The product key is no longer on the COA sticker to help prevent theft. Whenever you need to reset or reinstall the same operating system on your OEM PC, the product key will automatically be applied and activated. Depending on how you got your copy of Windows 10, you'll need either a 25-character product key or a digital license to activate it.

A digital license is a method of activation in Windows 10 that doesn't require you to enter a product key. All HP computers and tablets shipped with Windows 10 will activate automatically when connected to the internet. If you install a different version of Windows 10, the system might need to reactivate Windows. There might also be situations when Windows requires reactivation even though the product has already been activated. The W-series laptops were launched in 2008, at the same time as the Intel Centrino 2, marking an overhaul of Lenovo's product lineup.

Volume Of A Sphere Derivation Integral

A three-dimensional solid of revolution results from revolving a two-dimensional region about a particular axis or line called the axis of revolution. We can use a definite integral to find the volume of such a solid by taking slices perpendicular to the axis of revolution. The slices will be circular disks or washers. As a very elementary example, consider a cylinder of radius 2 and height 3, as pictured in Figure \(\PageIndex\).

Also recall the chapter opener, which showed the opera house l'Hemisphèric in Valencia, Spain. It has four sections with one of the sections being a theater in a five-story-high sphere under an oval roof as long as a football field. Inside is an IMAX screen that changes the sphere into a planetarium with a sky full of twinkling stars. Using triple integrals in spherical coordinates, we can find the volumes of different geometric shapes like these.

So far, our examples have all concerned regions revolved around the x\text[/latex] but we can generate a solid of revolution by revolving a plane region around any horizontal or vertical line. Using this method, Archimedes was able to show that a cone had the same volume as a a pyramid with the same base area and height. Express the volume of the solid inside the sphere and outside the cylinder as triple integrals in cylindrical coordinates and spherical coordinates, respectively. As stated before, spherical coordinate systems work well for solids that are symmetric around a point, such as spheres and cones.

Let us look at some examples before we consider triple integrals in spherical coordinates on general spherical regions. Consider the region inside the right circular cylinder with equation bounded below by the -plane and bounded above by the sphere with radius centered at the origin (). Set up a triple integral over this region with a function in cylindrical coordinates.

Determine an expression involving one or more definite integrals whose value is the volume of the solid of revolution generated by revolving the region \(R\) about the \(y\)-axis. We first want to find the volume of the balloon. If we look at the top part and the bottom part of the balloon separately, we see that they are geometric solids with known volume formulas. However, it is still worthwhile to set up and evaluate the integrals we would need to find the volume.

If we calculate the volume using integration, we can use the known volume formulas to check our answers. This will help ensure that we have the integrals set up correctly for the later, more complicated stages of the project. Triple integrals can often be more readily evaluated by using cylindrical coordinates instead of rectangular coordinates. Some common equations of surfaces in rectangular coordinates along with corresponding equations in cylindrical coordinates are listed in . These equations will become handy as we proceed with solving problems using triple integrals. In each of the following questions, draw a careful, labeled sketch of the region described, as well as the resulting solid that results from revolving the region about the stated axis.

In addition, draw a representative slice and state the volume of that slice, along with a definite integral whose value is the volume of the entire solid. It is not necessary to evaluate the integrals you find. In the preceding section, we used definite integrals to find the area between two curves. In this section, we use definite integrals to find volumes of three-dimensional solids.

We consider three approaches—slicing, disks, and washers—for finding these volumes, depending on the characteristics of the solid. For now, we are only interested in solids, whose volumes are generated through cross-sections that are easy to describe. In this project we use triple integrals to learn more about hot air balloons.

The top of the balloon is modeled by a half sphere of radius feet. The bottom of the balloon is modeled by a frustum of a cone . The radius of the large end of the frustum is feet and the radius of the small end of the frustum is feet. A graph of our balloon model and a cross-sectional diagram showing the dimensions are shown in the following figure. Consider the region inside the right circular cylinder with equation bounded below by the -plane and bounded above by Set up a triple integral with a function in cylindrical coordinates. Cylindrical coordinate systems work well for solids that are symmetric around an axis, such as cylinders and cones.

Let us look at some examples before we define the triple integral in cylindrical coordinates on general cylindrical regions. A similar situation occurs with triple integrals, but here we need to distinguish between cylindrical symmetry and spherical symmetry. In this section we convert triple integrals in rectangular coordinates into a triple integral in either cylindrical or spherical coordinates. For solids of revolution, the volume slices are often disks and the cross-sections are circles. The method of disks involves applying the method of slicing in the particular case in which the cross-sections are circles, and using the formula for the area of a circle. Suppose that the region \(R\) is revolved around the \(x\)-axis.

Set up a definite integral whose value is the exact volume of the solid of revolution that is generated. Use technology appropriately to evaluate the integral you find. It is possible to revolve a region around any horizontal or vertical line. Doing so adjusts the radii of the cylinders or washers involved by a constant value.

A careful, well-labeled plot of the solid of revolution will usually reveal how the different axis of revolution affects the definite integral. The concept of triple integration in spherical coordinates can be extended to integration over a general solid, using the projections onto the coordinate planes. Note that and mean the increments in volume and area, respectively. The variables and are used as the variables for integration to express the integrals.

We can use triple integrals and spherical coordinates to solve for the volume of a solid sphere. ¶We have seen how to compute certain areas by using integration; we will now look into how some volumes may also be computed by evaluating an integral. Generally, the volumes that we can compute this way have cross-sections that are easy to describe. For example, circular cross-sections are easy to describe as their area just depends on the radius, and so they are one of the central topics in this section.

However, we first discuss the general idea of calculating the volume of a solid by slicing up the solid. Suppose we divide each interval into subdivisions such that and Then we can state the following definition for a triple integral in cylindrical coordinates. Some solids of revolution have cavities in the middle; they are not solid all the way to the axis of revolution. Sometimes, this is just a result of the way the region of revolution is shaped with respect to the axis of revolution. In other cases, cavities arise when the region of revolution is defined as the region between the graphs of two functions.

Volume Of A Sphere Derivation A third way this can happen is when an axis of revolution other than the x\text[/latex] or y\text[/latex] is selected. Set up a definite integral whose value is the exact volume of the solid of revolution generated by revolving \(R\) about the \(y\)-axis. Set up a definite integral whose value is the exact volume of the solid of revolution generated by revolving \(R\) about the \(x\)-axis.

A definite integral may be used to represent the volume of a solid. The idea is to slice the solid into thin shapes whose volume is easy to calculate. The volume of each slice is found by taking the area of the cross-section and multiplying it by the width. Summing up the volumes of the slices and taking the limit as the width \(\rightarrow 0 \) results in an integral representing the volume. Consider a circular cone of radius 3 and height 5, which we view horizontally as pictured in Figure6.17. Our goal in this example is to use a definite integral to determine the volume of the cone.

A thin rectangle in the region between two curves. A representative disk formed by revolving the rectangle about the x -axis . The region between the curves over the given interval.

When either of the above area is rotated about its axis of rotation, then the solid of revolution that is created has a hole on the inside — like a distorted donut. If we now slice the solid perpendicular to the axis of rotation, then the cross-section shows a disk with a hole in it as indicated below. Such a disk looks like a "washer" and so the method that employs these disks for finding the volume of the solid of revolution is referred to as the Washer Method. The following example demonstrates how to find a volume that is created in this fashion. Note that and (Refer to Cylindrical and Spherical Coordinates for a review.) Spherical coordinates are useful for triple integrals over regions that are symmetric with respect to the origin. For the following exercises, draw the region bounded by the curves.

Then, use the washer method to find the volume when the region is revolved around the y[/latex]-axis. As with the disk method, we can also apply the washer method to solids of revolution that result from revolving a region around the y[/latex]-axis. A representative disk formed by revolving the rectangle about the x\text.[/latex] The region between the curves over the given interval. Use spherical coordinates to find the volume of the triple integral, where ??? Suppose instead that \(R\) is revolved around the \(y\)-axis. If possible, set up an integral expression whose value is the exact volume of the solid of revolution and evaluate the integral using appropriate technology.

We will also investigate one more application of definite integrals, to find the length of curves by again splitting the curve into small slices and adding up the smaller lengths. Then, use the washer method to find the volume when the region is revolved around the y-axis. As with the disk method, we can also apply the washer method to solids of revolution that result from revolving a region around the y-axis. A thin rectangle for approximating the area under a curve. The region under the curve is revolved about the x -axis , x -axis , resulting in the solid of revolution. Let us now turn towards the calculation of such volumes by working through two examples.

The right pyramid with square base shown in Figure 3.11 has cross-sections that must be squares if we cut the pyramid parallel to its base. The following example makes use of these cross-sections to calculate the volume of the pyramid for a certain height. Archimedes invented a method that was later re-discovered and became known as Cavalieri's principle. This involves slicing solids with a family of parallel planes.

In particular, if we have two solids and if each plane cuts them both into cross-sections of equal area, then the two solids have equal volumes. One of the most remarkable and important mathematical results obtained by Archimedes was the determination of the volume of a sphere. Archimedes used a technique of sub-dividing the volume into slices of known cross-sectional area and adding up, or integrating, the volumes of the slices. This was essentially an application of a technique that was — close to two thousand years later — formulated as integral calculus. Use the conversion formulas to write the equations of the sphere and cone in spherical coordinates. A spherical volume can be assumed to be constituted of a large number of thin circular disks of continuously varying radii kept over one another with their centres collinear.

We have to choose one of these elementary disks. A thin disk element of radius r and thickness dy located at a distance of y from the horizontal axis has been focused. Its volume can be written as the multiplication of base area πr² and thickness dy. Further, the disc radius r can be expressed in terms of vertical dimension y using the Pythagoras theorem.

Consider a circular cone of radius 3 and height 5, which we view horizontally as pictured in Figure \(\PageIndex\). Our goal in this activity is to use a definite integral to determine the volume of the cone. Then, use the disk method to find the volume when the region is rotated around the x[/latex]-axis. A representative disk formed by revolving the rectangle about the x\text\text[/latex] The region under the curve is revolved about the x\text,[/latex] resulting in the solid of revolution.

First of all, you may ask why I used cartesian coordinates to compute a result about spheres. And the answer is that I certainly tried to derive higher-dimensional spherical coordinates. I was able to derive the correct coordinates for dimensions 4 and 5.

However, I was unable to come up with a systematic way of determining how the new angles I introduced were parameterized. My naïve attempts to answer these questions gave me nonsense results for the volumes, so I had to find another way. The volume of sphere is measured in cubic units, such as m3, cm3, in3, etc. The shape of the sphere is round and three-dimensional.

It has three axes as x-axis, y-axis and z-axis which defines its shape. All the things like football and basketball are examples of the sphere which have volume. The unit of volume of a sphere is given as the 3. The metric units of volume are cubic meters or cubic centimeters while the USCS units of volume are, cubic inches or cubic feet. The volume of sphere depends on the radius of the sphere, hence changing it changes the volume of the sphere.

There are two types of spheres, solid sphere, and hollow sphere. The volume of both types of spheres is different. We will learn in the following sections about their volumes. This method for finding the volume of a solid of revolution generated by two curves is often called the washer method. Then, use the disk method to find the volume when the region is rotated around the x-axis. But we can generate a solid of revolution by revolving a plane region around any horizontal or vertical line.

In the next example, we look at a solid of revolution that has been generated by revolving a region around the y-axis.y-axis. It is far from obvious from the figure above how the cone and sphere add up to the cylinder. However, if we `rearrange' the conic volume, things become clearer. We note that a cone with half the height () has half the volume.

So, we replace the cone by a double cone, each half of height , with centre-point at the centre of the sphere . Now it is clear that in a horizontal slice, the cross-section of the sphere is greatest at the equator and least at the poles. Contrariwise, the cross-section of the cone is greatest near the top and bottom, and least near the centre-point. Thus, it is not unreasonable to speculate that the sum of the two cross-section areas might be equal. With the polar coordinate system, when we say , we mean a circle of radius units and when we mean an infinite ray making an angle with the positive -axis.