Question

The largest sphere is carved out of a solid cube of side 21 cm. Find the volume of the sphere.

Answer 1

The largest sphere that can be carved out of a solid cube of side 21 cm means diameter of sphere will be 21 cm.

Therefore, radius of sphere, r = `21/2` cm

Now, Volume of sphere = `4/3` πr³

= `4/3 xx 22/7 xx (21/2)^3`

= `(4 xx 22 xx 21 xx 21 xx 21)/(7 xx 3 xx 2 xx 2 xx 2)`

= 11 × 21 × 21

= 4851 cm³