Question

A sphere of radius r is inscribed inside a cube. The volume enclosed between the cube and the sphere is: ​

Answer 1

Answer:

Volume enclosed between cube and sphere is

Step-by-step explanation:

Given: Radius of Sphere = r

           Sphere inscribed in Cube

To find: Volume enclosed between cube and sphere

Length of edge of cube, a = 2 × r = 2r

Volume enclosed between cube and sphere

= volume of cube -  volume of Sphere

$=\:a^3-\frac{4}{3}\pi r^3$

$=\:(2r)^3-\frac{4}{3}\pi r^3$

$=\:8r^3-\frac{4}{3}\pi r^3$

$=\:(8-\frac{4}{3}\times\frac{22}{7})r^3$

$=\:\frac{168-88}{21}r^3$

$=\:\frac{80}{21}r^3$

Therefore, Volume enclosed between cube and sphere is $\:\frac{80}{21}r^3$