Question

The number of solid spheres, of diameter 6 cm each, that could be moulded to form a solid metallic cylinder of height 45 cm and diameter 4 cm is
(a) 3
(b) 4
(c) 5
(d) 6

Answer 1

(c) 5

Radius of sphere = $\frac{6}{2}=3\mathrm{cm}$
Volume of sphere$=\frac{4}{3}\mathrm{\pi }{r}^3$
$=\left(\frac{4}{3}\times \mathrm{\pi }\times 3\times 3\times 3\right){\text{cm}}^3$

Radius of cylinder = $\frac{4}{2}=2\mathrm{cm}$

Height of cylinder = 45 cm

Volume of each cylinder$=\mathrm{\pi }{r}^{2}h$
$=\left(\mathrm{\pi }\times 2\times 2\times 45\right){\text{cm}}^3$

Number of solid spheres$=\frac{\text{Volume of the cylinder}}{\text{Volume of each sphere}}$

$$\begin{gathered} =\frac{\mathrm{\pi }\times 2\times 2\times 45\times 3}{4\times \mathrm{\pi }\times 3\times 3\times 3} \\ =5 \end{gathered}$$