The number of solid spheres ,each of diameter 3 cm that could be moulded  to form a solid metal cylinder of height 54cm and diameter 4 cm is?

Solution:

Diameter of sphere = 3 cm → Radius = 1.5 cm
Diameter of cylinder = 4 cm → Radius = 2 cm
Height of cylinder = 54 cm

Volume of one sphere:
$$ V_s = \frac{4}{3} \pi (1.5)^3 = 4.5\pi\ \text{cm}^3 $$
Volume of cylinder:
$$ V_c = \pi (2)^2 (54) = 216\pi\ \text{cm}^3 $$
Number of spheres:
$$ \text{Number} = \frac{V_c}{V_s} = \frac{216\pi}{4.5\pi} = 48 $$

∴ The required number of spheres = 48.