Question

Question 3
A cone is 8.4cm high and the radius of its base is 2.1cm. 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

The answer is B.
Given, height of the cone = 8.4 cm

Radius of the base = 2.1 cm
Volume of a cone $=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\times \pi \times (2.1{)}^2\times 8.4$
$=\pi \times 4.41\times 2.28c{m}^3$

The cone is melted and recast into a sphere.

Let the radius of a sphere be R.

Then, volume of the sphere = volume of the cone

$\Rightarrow \frac{4}{3}\pi r^3=\pi \times 4.41\times 2.8\Rightarrow r^3=\frac{4.41\times 2.8\times 3}{4}$

$\Rightarrow r^3=4.41\times 0.7\times 3$

$\Rightarrow r^3=4.41\times 2.1$

$\therefore r=2.1$

Hence, the radius of the sphere is 2.1 cm.