Question

A spherical solid material of radius $18cm$ is melted and recast into three small solid spherical spheres of different sizes. If the radii of two spheres are $2cm$ and $12cm$, find the radius of the third sphere.

Answer 1

R.E.F image

Volume of sphere with radius $18cm=\frac{4}{3}\pi r^3$

$V=\frac{4}{3}\times \frac{22}{7}\times {18}^3$

$=24438.85c{m}^3$

Similarly volume of sphere of radius $2cm$

$V_1=\frac{4}{3}\times \frac{22}{7}\times 2^3$

$=33.528c{m}^3$

Volume of sphere of radius with radius $12cm$

$V_2=\frac{4}{3}\times \frac{22}{7}\times {12}^3$

$=7241.14c{m}^3$

Let the volume of the third sphere be $V_3$

a/c question

$V=V_1+V_2+V_3$

$\Rightarrow V_3=V-(V_1+V_2)$

$=24438.85-(33.52+7241.14)$

$=17164.187c{m}^3$

Let the radius of small sphere be $r_3$

then $V_3=\frac{4}{3}\pi r^3$

$\Rightarrow 17164.187=\frac{4}{3}\times \frac{22}{7}\times r^3$

$17164.187=4.190r^3$

$4096.4646=r^3$

$\Rightarrow r=16.0006$