A sphere and a hemisphere have the same surface area. the ratio of their volumes is ?
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Answer:
let R and r be the radii of sphere and hemisphere respectively.
Step-by-step explanation:
let area of both be 100
4πR^2 = 100 => πR^2 = 25
R = 5/√π
2πr^2 = 100 => r = 5√2/√π
volume ratio = 4/3πR^3 : 2/3πr^3
=[ 4/3π (5/√π)^3 : [2/3 π(5√2/√π)^3
= (2 × 125) : (250√2) = 1 : √2
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