Question

A cone is 8.4 cm high and the radius of its base is 2.1 cm. It is melted and recast into a sphere. The radius of the sphere is
(a) 4.2 cm
(b) 2.1 cm
(c) 2.4 cm
(d) 1.6 cm

Answer 1

(b) 2.1 cm

Let r cm be the radius of the sphere.
Volume of the cone = volume of the sphere
$$\begin{gathered} \Rightarrow \frac{1}{3}\mathrm{\pi }\times 2.1\times 2.1\times 8.4=\frac{4}{3}\mathrm{\pi }{r}^3 \\ \Rightarrow r^3=2.1\times 2.1\times 2.1 \\ \Rightarrow r=2.1\mathrm{cm} \end{gathered}$$