Question

A metallic cylinder of radius 8 cm and height 2 cm is melted and converted into a right circular cone of height 6 cm. The radius of the base of this cone is
(a) 4 cm
(b) 5 cm
(c) 6 cm
(d) 8 cm

Answer 1

(d) 8 cm
Radius of the cylinder = 8 cm
Height of the cylinder = 2 cm
Height of the cone = 6 cm

Volume of the cylinder = Volume of the cone
Therefore,
$$\begin{gathered} \mathrm{\pi }\times 8\times 8\times 2=\frac{1}{3}\mathrm{\pi }\times r^2\times 6 \\ \Rightarrow 128=r^2\times 2 \\ \Rightarrow r^2=\frac{128}{2} \\ \Rightarrow r^2=64 \\ \Rightarrow r=8\text{cm} \end{gathered}$$
Hence, the radius of the base of the cone is 8 cm.