Question

A metallic cone of base radius 2.1 cm and height 8.4 cm is melted and moulded into a sphere. The radius of the sphere is
(a) 2.1 cm
(b) 1.05 cm
(c) 1.5 cm
(d) 2 cm

Answer 1

(a) 2.1 cm
Radius of cone = 2.1 cm
Height of cone = 8.4 cm

Volume of cone = $\frac{1}{3}{\mathrm{\pi r}}^2\mathrm{h}=\frac{1}{3}\mathrm{\pi }{\left(2.1\right)}^2\times 8.4$

Volume of the sphere$=\frac{4}{3}\mathrm{\pi }{r}^3$
Therefore,

Volume of cone = Volume of sphere

$$\begin{gathered} \Rightarrow \frac{1}{3}\mathrm{\pi }\times {\left(2.1\right)}^2\times 8.4=\frac{4}{3}\mathrm{\pi }{r}^3 \\ \Rightarrow 4.41\times 8.4=4r^3 \\ \Rightarrow 37.044=4r^3 \\ \Rightarrow r^3=\frac{37.044}{4} \\ \Rightarrow r^3={\left(2.1\right)}^3 \\ \Rightarrow r=2.1\text{cm} \end{gathered}$$

Hence, the radius of the sphere is 2.1 cm.