Surface area of sphere - Mathematics
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The document discusses the surface area of a sphere, highlighting that it is not equal to that of a cylinder despite visual similarities. It presents Archimedes' proof that the surface area of a sphere is equal to the lateral surface area of a cylinder, specifically stating the formula as 4πr². Additionally, it offers a commercial context for Letstute, an e-learning company, promoting their educational resources.
Surface area of sphere - Mathematics
- 1. Surface Area of Sphere
- 3. Are they equal ?
- 4. No they are not equal
- 6. • No edges or vertices. • The entire curved surface is considered as one surface.
- 7. Now, lets calculate the surface area of sphere
- 8. Let’s compare a sphere with radius ‘r’ with a cylinder of the same radius.
- 9. Now when we insert the sphere into the cylinder, we can see that the height of cylinder = diameter of the sphere i.e h = d = 2 r
- 10. Then proof of this was given to us by the famous mathematician Archimedes and it says that , Surface Area of sphere = lateral surface area of cylinder
- 11. Proof
- 12. We can also say that, Surface area of sphere = 4 times area of circle
- 13. A sphere is a 3 – D object Lateral surface area of cylinder equals surface area of Sphere Surface area of sphere is 4 𝜋𝑟2 Surface area of sphere = 4 (Area of a circle)
- 14. If a football of diameter 22 cm is to be made then how much of leather sheet will it need?
- 15. If a football of diameter 22 cm is to be made then how much of leather sheet will it need?
- 16. When we cut a sphere, we get hemisphere Surface area of hollow hemisphere = 2 𝜋𝑟2
- 17. Surface area of solid hemisphere = 3 𝜋𝑟2
- 18. Q. Find the surface area of a solid hemisphere with radius 5 cm. Ans: 235.5 𝑐𝑚2
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