Question

a cube of side4cm contain a sphere touching its sides . find the volume of the gap in betweena cube of side4cm contain a sphere touching its sides . find the volume of the gap in between

Answer 1

Let's start with the cube of 4cm.

Vc = L* W * H

Vc = 4 * 4 * 4 = 64 cu.cm

now to find the volume of the cylinder

Vcy = pi r^2 h

the diameter is 4cm and 2 * r(adius)

d = 2r

4 = 2r

r = 2 cm

volume of the cylinder is

Vcy = pi * 2^2 * 4

Vcy = 16 pi = 50.265 cu. cm

The region not in the cylinder but in the cube is

Vc - Vcy

Vregion = 64 - 50.265

Vregion = 13.735 cu. cm

Answer 2

Side of cube = 4 cm

Volume of cube = 4 x 4 x 4 = 64cm³

The sphere touches the cube 's sides. So, diameter of cube = 4 cm.

Radius = 2cm

So, volume of sphere = 4/3 pi r³ = 33.51cm³ (approximately)

So, volume of the gap = V of cube - V of sphere= 64-33.51 = 30.49 cm³

Hope it helps!