Question

A sphere of diameter 15.6 cm is melted and into a right circular cone of height 31.2 cm.Find the diameter of the base of the cone.

Answer 1

Sol:
Diameter of a sphere = 15.6 cm
Radius of the sphere = $\frac{15.6}{2}$ = 7.8 cm

Volume of a sphere = $\frac{4}{3}$$\pi$$r^3$
Volume of the sphere = $\frac{4}{3}$ $\times$$\frac{22}{7}$ $\times 7.8\times 7.8\times 7.8$

Height of the cone = 31.2 cm
Let the radius of the cone be 'r' cm.

Volume of a cone = $\frac{1}{3}$$\pi$$r^2$h
Volume of the cone = $\frac{1}{3}$ $\times$$\frac{22}{7}$ $\times r^2\times 31.2$

Volume of the cone = Volume of the sphere
$\frac{1}{3}$ $\times$$\frac{22}{7}\times$ $r^2\times 31.2$ = $\frac{4}{3}$ $\times$$\frac{22}{7}$ $\times 7.8\times 7.8\times 7.8$
⇒ $r^2$ = $(7.8{)}^2$
⇒ r = 7.8 cm

Radius of the cone = 7.8 cm
∴ Diameter of the cone = 2 $\times$ 7.8 = 15.6 cm