Question

The base radius and height of a right circular solid cone are 2 cm and 8 cm respectively. It is melted and recast into spheres of diameter 2 cm each. Find the number spheres formed?​

Answer 1

Given :-

• Base radius of the right circular solid cone = 2 cm

• Height of the right circular solid cone = 8 cm

• Diameter of the sphere = 2 cm

To Find :-

• Number of spheres.

Solution :-

Let number of spheres be n.

Radius of the sphere = 2/2 = 1 cm

$\bf Volume \ of \ right \ circular \ cone = \dfrac{1}{3} \pi r^2h$

$\longrightarrow \sf \dfrac{1}{3} \times \pi \times 2 \times 2 \times 8 \\\\\longrightarrow \sf \dfrac{1}{3} \times \pi \times 32\\\\\longrightarrow \dfrac{32}{3}\pi$

$\bf Volume \ of \ a \ sphere = \dfrac{4}{3} \pi r^3$

$\longrightarrow\sf \dfrac{4}{3} \times \pi \times 1\times 1 \times 1 \\\\\longrightarrow \dfrac{4}{3} \pi$

According to the question :-

Volume of right circular cone = n × Volume of a sphere

$\longrightarrow\sf \dfrac{32}{3}\pi = n \times \dfrac{4}{3} \pi \\\\\longrightarrow \dfrac{32}{3} = n \times \dfrac{4}{3} \\\\\longrightarrow n = \dfrac{32}{3} \times \dfrac{3}{4} \\\\\longrightarrow n = \dfrac{32}{4} \\\\\longrightarrow \bf n = 8$

Number of spheres = 8