Question

A speher, a cylinder and a cone are of the same radius and same height find the ratio of the curved surface area

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Answer 1

Step-by-step explanation:

Given that,

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

Then,

The height of the sphere is the diameter of sphere i.e. 2r. Since the height of sphere, cylinder and cone are same so the height of cylinder and cone will also be 2r.

Now,

C.S.A. of sphere = 4πr²

C.S.A. of cylinder = 2πrh

= 2πr×2r

= 4πr²

C.S.A. of cone = πrl

= πr√(h²+r²)

= πr√{(2r)²+r²}

= πr√(4r²+r²)

= πr√(5r²)

= πr×r√5

= √5πr²

Thus,

The ratio of C.S.A. of a sphere, a cylinder and a cone = 4πr² : 4πr² : √5πr²

= 4 : 4 : √5