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Question

The surface areas of a cube and a sphere are equal. Calculate the ratio of their volumes.

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Solution

Let the side of the cube=a

So, the surface area of the cube=6a2

Let the radius of the sphere=r

So, the surface area of the sphere =4πr2


Therefore,

6a2=4πr2 =x(let)


Therefore,

a=x6

And r=x4π

Therefore, ratio of their volumes,

=a343πr3

=(x6)343π(x4π)3

=161643π14π14π

=124π6

=4π24

=π6

So, the ratio is π:6.


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