A cylinder made out of lead has radius 4 cm and height 10 cm. It is melted to form lead shots of radius 2 cm. Find the number of lead shots.

Radius of each lead shot = r_s = 2 cm

Radius of cylinder = r_c = 4 cm

Height of cylinder = h = 10 cm

volume of sphere = πr_s³

Volume of cylinder= πr_c²h

The lead shots area made by melting the cylinder which means same melted volume is used to make the lead shots thus the volume remains the same

Let ‘n’ be the number of lead shots formed

i.e. volume of n lead shots = volume of cylinder

⇒ n × πr_s³ = πr_c²h

⇒ 4 × r_s³ × n = 3 × r_c² × h

Substituting values

⇒ 4 × 2³ × n = 3 × 4² × 10

⇒ 4 × 8 × n = 3 × 16 × 10

⇒ 4 × n = 3 × 2 × 10

⇒ 4 × n = 3 × 20

⇒ n = 3 × 5

⇒ n = 15

Number of lead shots made = 15