A-sphere-of-radius-r-contains-a-cube-inside-it-All-the-vertices-of-the-cube-touch-the-surface-of-sphere-What-is-the-volume-of-the-cube-

Question Number 5319 by Rasheed Soomro last updated on 07/May/16

A sphere of radius r contains a cube

inside it . All the vertices of the cube

touch the surface of sphere .

What is the volume of the cube ?

Answered by Rasheed Soomro last updated on 08/May/16

Commented by Rasheed Soomro last updated on 08/May/16

{Let}^{'} s cut the “ sphered {cube}^{″} in two

equal parts in such a manner that two

dimensions of the cube are preserved .

Above is the cross - section of one of

the two parts . r is radius of the sphere

and s is measure of the side of the cube .

clearly,

s = \sqrt{r^{2} + r^{2}} = \sqrt{2} r

volume v of the cube

v = s^{3} = {(\sqrt{2} r)}^{3} = 2 \sqrt{2} r^{3}