Question

22 A sphere, a cylinder and a cone are the same radius and same height. Find the
ratio of their curved surfaces.​

Answer 1

Answer:

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Answer 2

Given:

A sphere, a cylinder and a cone are the same radius and same height.

To find out:

Find the ratio of their curved surfaces ?

Solution:

Let r be the common radius of sphere, a cone and a cylinder.

Then,

Height of cone = height of cylinder = height of sphere = 2r

Let l be the slant height of the cone. Then,

$\sf{ \: \: \: \: \: \: l = \sqrt{ {r}^{2} + {h}^{2} }} \\ \implies \sf{l = \sqrt{ {r}^{2} + {4r}^{2}} } \\ \implies \sf{l = \sqrt{ {5r}^{2} } }$

Now,

S₁ = curved surface area of sphere =4πr²

S₂ = curved surface area of cylinder = 2πr ⨯ 2r = 4πr²

S₃ = curved surface area of cone = πrl = πrl ⨯ √5r = √5πr²

Therefore,

S₁ : S₂ : S₃ = 4πr² : 4πr² : √5πr² = 4 : 4 : √5