Twelve solid hemispheres of the same size are melted and recast to in a right circular cylinder of diameter 7 cm and height 28 cm. What is the radius of the hemispheres?

3.5 cm

We know that,

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

The volume of a cylinder = πR²h 

We have,

Diameter of the cylinder = 7 cm

then the radius = \(\frac{7}{2}\)

Height of the cylinder = 28 cm

According to the question,

12 × The volume of a hemisphere = The volume of a cylinder 

= 12 × \(\frac{2}{3}\) × π × r³ = π × R² × h

= r³ = \(\frac{343}{8}\)

= r = \(\frac{7}{2}\) = 3.5 cm