Question

A solid metallic sphere of diameter 21 cm is melted and recast into a number of smaller cones, each of diameter 3.5 cm and height 3 cm. Find the number of cones so formed.

Answer 1

Diameter of the sphere = 21 cm

So, radius of sphere $=\frac{21}{2}$

Radius of sphere = 10.5 cm

Volume of sphere $=\frac{4}{3}\pi r^3=\frac{4}{3}\times \frac{22}{7}\times 10.5\times 10.5\times 10.5=4851c{m}^3$

Diameter of cone = 3.5 cm

So, radius of cone $=\frac{3.5}{2}$

Radius of cone = 1.75 cm

Volume of cone $=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\times \frac{22}{7}\times 1.75\times 1.75\times 3=9.625c{m}^3$

Number cones formed $=\frac{4851}{9.625}=504$