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Prove that the surface area of a sphere ...

Prove that the surface area of a sphere is equal to the curved surface area of the circumscribed cylinder.

Text Solution

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For the circumscribing cylinder, height` =2r,` radius` =r` C.S.A`=2πrl=2π(2r)r=4πr^2 ` which is nothing but total surface area of the sphere.
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Knowledge Check

  • The ratio of the surface area of a sphere and the curved surface area of the cylinder circumscribing the sphere is

    A
    `1:2`
    B
    `1:1`
    C
    `2:1`
    D
    `2:3`

  • The lateral surface area of a cylinder is

    A
    `pi r^(2)h`
    B
    `pi rh`
    C
    `2 pi rh`
    D
    `2 pi r^(2)`

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