A solid metal cylinder of radius 14 cm and height 21 cm is melted down and recast into spheres of radius 3.5 cm. Calculate the number of spheres that can be made.

Radius of a solid metallic cylinder (r) = 14 cm,

Height (h) of cylinder = 21 cm.

Radius of sphere (R) = 3.5 cm.

Let the number of spheres formed be n.

Volume of metal cylinder = n × Volume of each sphere.

$\therefore πr^2h = n \times \dfrac{4}{3}πR^3 \\[1em] \Rightarrow r^2h = n \times \dfrac{4}{3}R^3 \text{ (Dividing both sides by π)} \\[1em] \Rightarrow (14)^2 \times 21 = n \times \dfrac{4}{3} \times (3.5)^3 \\[1em] \Rightarrow n = \dfrac{14^2 \times 3 \times 21}{4 \times (3.5)^3} \\[1em] \Rightarrow n = \dfrac{12348}{171.5} \\[1em] \Rightarrow n = 72.$

Hence, the number of spheres that can be made from solid cylinder are 72.