24 equal solid hemispheres are melted to form a right circular cylinder of radius 12 cm and height 24 cm. Find the radius of each solid hemisphere.

6 cm

We know that,

The volume of a hemisphere = \(\frac{2}{3}\) πr³

The volume of the cylinder = πr²h

We have,

Number of solid hemispheres = 24

Radius of the cylinder = 12 cm

Height of the cylinder = 24 cm

The total volume of the 24 solid hemispheres = The volume of the cylinder.

The volume of the cylinder =  π(12 cm)²24 = 144 × 24π

Since the 24 solid hemispheres have the same volume as the cylinder, the volume of each hemisphere can be calculated as: 

Now,  24 × \(\frac{2}{3}\) πr³ = 144 × 24π

\(\frac{2}{3}\) r³ = 144

r³ = 216

r = 6