Question

the surface area of sphere is equal to the surface area of cube. find the ratio of their volumes​

Answer 1

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Answer 2

surface area of a cube = 6a^2

surface area of a sphere = 4πr^2

Therefore 6a^2 = 4πr^2

r/a = √3/√(2π)

volume of a sphere=4/3πr^3

volume of a cube=a^3

[4πr^3/3]/a^3

=(4π/3)*(r/a)^3

=(4π*3√3)/(3*2π√(2π))

=(12π√3)/(6π√(2π))

=√2*√3/√π

=√6/√π

therefore the ratio of their volumes is √6:√π

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