Question

A metallic sphere of radius $10.5cm$ is melted and thus recast into small cones, each of radius $3.5cm$ and height $3cm$. Find how many cones are obtained.

Answer 1

Given,

Radius of metallic sphere $R=10.5cm$

Radius of circular base of smaller cone $r=3.5cm$

Hight of cone $h=3cm$

Volume of metallic sphere $V=\frac{4}{3}\pi R^3$

$=\frac{4}{3}\times \frac{22}{7}\times (10.5{)}^{3}c{m}^3$

$=\frac{4}{3}\times \frac{22}{7}\times 1157.625c{m}^3$

$=\frac{88}{21}\times 1157.625c{m}^3$

$=88\times 55.125c{m}^3$

Volume of metallic sphere $V=4851c{m}^3$

Volume of one cone $v=\frac{1}{3}\pi r^{2}h$

$=\frac{1}{3}\times \frac{22}{7}\times (3.5{)}^2\times 3c{m}^3$

$=\frac{22}{7}\times 12.25c{m}^3$

Volume of one cone$=38.5c{m}^3$

Number of cones formed $n=\frac{\text{Volume of sphere(V)}}{\text{Volume of one cone (v)}}$

$n=\frac{4851c{m}^3}{38.5c{m}^3}$

$n=126$

Hence the solid sphere can be melted in $126$ smaller cones .