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
Solution:
(b) 2.1 cm
Let r cm be the radius of the sphere.
Volume of the cone = volume of the sphere
$\Rightarrow \frac{1}{3} \pi \times 2.1 \times 2.1 \times 8.4=\frac{4}{3} \pi r^{3}$
$\Rightarrow r^{3}=2.1 \times 2.1 \times 2.1$
$\Rightarrow r=2.1 \mathrm{~cm}$