Question

A sphere of diameter 12.6 cm is melted and cast into a right circular cone of height 25.2 cm. The radius of the base of the cone is
(a) 6.3 cm
(b) 2.1 cm
(c) 6 cm
(d) 4 cm

Answer 1

(a) 6.3 cm
Let r cm be the radius of base of the cone.
Volume of the sphere = volume of the cone
$$\begin{gathered} \Rightarrow \frac{4}{3}\mathrm{\pi }\times {\left(6.3\right)}^3=\frac{1}{3}\mathrm{\pi }\times r^2\times 25.2 \\ \Rightarrow r^2=\frac{4\times 6.3\times 6.3\times 6.3}{25.2}=39.69 \\ \Rightarrow r=\sqrt{39.69}=6.3\mathrm{cm} \end{gathered}$$