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Maths-

General

Easy

Question

A Sphere and cube have the same surface. Show that the ratio of the volume of the sphere to that of the cube is $square root of 6 colon square root of pi$

hint Hint:

Volume of a sphere $equals 4 over 3 pi r cubed$
Volume of cube a³

The correct answer is: √6:√π

Explanation:

We have given a sphere and a cube with same surface area.

We have to prove that there ratio of volume of the sphere to that cube is $square root of 6 colon square root of pi$

Step 1 of 1:
Let the radius of sphere and side of cube be r, a respectively.
So,
Surface area of sphere will be $4 pi r squared$ and surface area of cube be 6a²
It is given that both surface area are equal.
So,
$6 a squared equals 4 pi r squared$
$a equals square root of fraction numerator 4 pi over denominator 6 end fraction end root r$
Now the volume of sphere will be $V subscript s equals 4 over 3 pi r cubed$
And volume of cube will be
$V equals a cubed$
$equals open parentheses square root of fraction numerator 4 pi over denominator 6 end fraction end root r close parentheses cubed$
$equals fraction numerator 4 pi over denominator 6 end fraction square root of fraction numerator 4 pi over denominator 6 end fraction end root r cubed$
Now ratio of their volume will be

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