Question

The dimensions of a cuboid are 44 cm, 21 cm, 12 cm. It is melted and a cone of height 24 cm is made. Find the radius of its base.

Answer 1

The dimensions of the cuboid are 44 cm, 21 cm and 12 cm.

Let the radius of the cone be r cm.

Height of the cone, h = 24 cm

It is given that cuboid is melted to form a cone.

∴ Volume of metal in cone = Volume of metal in cuboid

$$\begin{gathered} \Rightarrow \frac{1}{3}\mathrm{\pi }{r}^{2}h=44\times 21\times 12\left(\mathrm{Volume}\mathrm{of}\mathrm{cuboid}=\mathrm{Length}\times \mathrm{Breadth}\times \mathrm{Height}\right) \\ \Rightarrow \frac{1}{3}\times \frac{22}{7}\times r^2\times 24=44\times 21\times 12 \\ \Rightarrow r=\sqrt{\frac{44\times 21\times 12\times 21}{22\times 24}}=\sqrt{21\times 21}=21\mathrm{cm} \end{gathered}$$
Thus, the radius of the base of cone is 21 cm.