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Surface area of sphere=surface area of cube. Find the ratio between their volume

Surface area of sphere=surface area of cube. Find the ratio between their volume

Grade:9

1 Answers

Pawan Prajapati
askIITians Faculty 8741 Points
9 months ago
Answer ::

surface area of a cube=6a2
surface area of a sphere =4πr2
6a2 =4πr2
r2/a2=6/4π
r/a=√3/√2√π
volume of a sphere=4/3πr3
volume of a cube=a3
4/3πr3 /a3
(4π/3) *(r/a)cube
4π/3*√3/√2√π*√3/√2√π*√3/√2√π
=2/√2√π
=√2/√π
therefore the ratio of their volumes is √2:√π

Thanks

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