Question

A solid piece of iron in the form a cuboid of dimensions (49 cm × 33 cm × 24 cm) is moulded into a solid sphere. The radius of the sphere is
(a) 19 cm
(b) 21 cm
(c) 23 cm
(d) 25 cm

Answer 1

(b) 21 cm
Volume of the cuboid $=\left(l\times b\times h\right)$ = $49\times 33\times 24c{m}^3$
Let the radius of the sphere be r cm.
Volume of the sphere$=\frac{4}{3}\mathrm{\pi }{r}^3$

The volume of the sphere and the cuboid are the same.
Therefore,

$$\begin{gathered} \frac{4}{3}\mathrm{\pi }{r}^3=49\times 33\times 24 \\ \Rightarrow \frac{4}{3}\times \frac{22}{7}\times r^3=49\times 33\times 24 \end{gathered}$$
$$\begin{gathered} \Rightarrow r^3=49\times 33\times 24\times \frac{21}{88} \\ \Rightarrow r^3=21\times 21\times 21 \\ \Rightarrow r^3={\left(21\right)}^3 \\ \Rightarrow r=21\text{cm} \end{gathered}$$

Hence, the radius of the sphere is 21 cm.