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Learn how to calculate the surface area of a sphere using calculus and Archimedes' hat-box theorem. See proofs, examples, and practice problems with solutions.
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Jan 16, 2024 · To find the surface area of a sphere, use the equation 4πr2, where r stands for the radius, which you will multiply by itself to square it. Then, multiply the squared radius by 4. For example, if the radius is 5, it would be 25 times 4, which equals 100.
- 1. Know the parts of the equation, Surface Area = 4πr. This nearly ancient formula is still the easiest way to determine the surface area of a sphe...
- 2. Find the radius of the sphere. Sometimes your problem will supply you the radius, and other times you will have to find it yourself. If you are...
- 3. Square the radius by multiplying it by itself. You can either do this by manually multiplying (5 = 5 * 5 = 25) or by using your calculator's "sq...
- 4. Multiply this result by 4. While you can multiply either 4 or pi first, it is generally easier to start with 4 since there are no decimals to mu...
- 5. Multiply the results by pi (π). If your problem says "exact value", write the symbol π after your number and call it done. Otherwise, use the ap...
- 6. Remember to add you units to the final answer. Is your sphere's surface area 314 inches big, or 314 miles (505 km) big? The units need to be wri...
- 7. Practice with an example. If the radius of a sphere is 7 centimeters, what is the surface area of that sphere? 4πr r = 7 4 * π * 7 49 * 4 * π 19...
- 8. Understand surface area. The surface area of a sphere is the area covering the outside of the sphere -- think of it as the rubber covering a kic...
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From a visual perspective, a sphere has a three-dimensional structure that forms by rotating a disc that is circular with one of the diagonals. Let us consider an instance where spherical ball faces are painted. To paint the whole surface, the paint quantity required has to be known beforehand. Hence, the area of every face has to be known to calcu...
The surface area of a sphere formula is given by, A = 4 π r2 square units For any three-dimensional shapes, the area of the object can be categorised into three types. They are: 1. Curved Surface Area 2. Lateral Surface Area 3. Total Surface Area Curved Surface Area: The curved surface area is the area of all the curved regions of the solid. Latera...
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Learn how to calculate the surface area of a sphere using the formula A = 4 π r2, where r is the radius of the sphere. See solved examples, FAQs and a quiz on this topic at BYJU'S.
Jul 19, 2024 · Learn how to find the area of a sphere using different formulas and quantities, such as radius, diameter, volume, and surface-to-volume ratio. Use the calculator to enter any parameter and get the result in various units.
- Dominik Czernia
Jun 11, 2023 · The surface area of a sphere is the entire region covered by its outer round surface. It is also the curved surface area of a sphere. Like all other surface area it is expressed in square units such as m 2, cm 2, and mm 2. We will learn how to find the surface area of a solid sphere. The equations are given below.
Learn how to calculate the surface area of a sphere using the formula Area = 4 π r 2 , where r is the radius of the sphere. See interactive diagrams, interesting facts and related topics on spheres and other shapes.
Learn how to find the surface area of a sphere using the formula A = 4πr^2, where r is the radius. See how to derive the formula from the curved surface area of a cylinder and solve some examples.
