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) 1.6 cm
(b) 2.1 cm
(c) 2.4 cm
(d) 4.2 cm

Answer 1

(b) 2.1 cm

Let r cm be the radius of the sphere.
Radius of the base of the cone = 2.1 cm
Height of the cone = 8.4 cm
The cone is melted and recast into a sphere.
Then volume of sphere = volume of cone

$$\begin{gathered} \Rightarrow \frac{4}{3}\mathrm{\pi }{r}^3=\frac{1}{3}\mathrm{\pi }\times {\left(2.1\right)}^2\times 8.4 \\ \Rightarrow r^{\mathit{3}}=\frac{2.1\times 2.1\times 8.4}{4}=2.1\times 2.1\times 2.1 \\ \Rightarrow r=2.1\mathrm{cm} \end{gathered}$$