Question

The largest sphere is carved out of a cube of edge p units.Find the volume

Answer 1

When sphere is carved out of a cube, diameter = side of cube.

Radius = p/2.

Volume of sphere = 4/3 × π × r³

= 4/3 × π × (p/2)³

= πp³/6

Answer 2

Answer:

$\frac{ \frac{4}{3} {p}^{3} \pi}{24}$

Step-by-step explanation:

Largest sphere is possible only when the sphere touches all the vertical sides.

So, Radius = p/2

Volume =

$\frac{4}{3} \pi {r}^{3}$

Putting r = (p/2)^3

We get the volume..