A sphere ,a cylinder and a cone are of the same radius and same height , find the ratio of CSAs

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Dear Student,

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

Let radius = r 

and, height = h

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



Hope it helps :)

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let the radius be r. Let the height by h.
The height of a sphere is the diameter = 2r

For sphere CSA = 4πr2
For cylinder CSA = 2πrh = 2πr(2r) = 4πr2
For cone CSA = πr x sqrt(r2 + h2) = πr x sqrt(r2 + (2r)2) = πr x sqrt(5r2) = πr x r x sqrt(5) = πr2sqrt(5)

From these 3, you get:
4πr: 4πr2 : πr2sqrt(5)
= 4 : 4 : sqrt(5)

 
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