Question

If a sphere is inscribed in a cube, find the ratio of the volume of the cube to the volume of the sphere.

Answer 1

Let edge of a cube = a

then its volume $=a^3$

$\because$ A sphere is inscribed in the cube

$\therefore$ Diameter of sphere $=a$

and radius $=\left(\frac{a}{2}\right)$

$\therefore Volumeofsphere=\frac{4}{3}\pi r^3$

$=\frac{4}{3}\pi {\left(\frac{a}{2}\right)}^2$

$=\frac{4}{3}\pi \times \frac{a^3}{8}$

$=\frac{\pi a^3}{6}$

Now ratio between their volumes

$=a^3:\frac{\pi a^3}{6}$

$=6a^3:\pi a^3$

$=6:\pi$