Question

The volume of a sphere is $4851c{m}^3$. How much should its radius be reduced so that its volume become $\frac{4312}{3}c{m}^3$?

Answer 1

We have

Volume of Sphere $=4851c{m}^3$

We know that, the volume of Sphere

$=\frac{4}{3}\pi R^3$

$\text{So,}$

$\frac{4}{3}\pi R^3=4851$

$R^3=\frac{3\times 485\times 7}{4\times 22}$

$R=\sqrt[3]{31157.625}$

$R=10.5cm.$

Now, for volume of the sphere $=\frac{4312}{3}c{m}^3$

$\frac{4}{3}\pi r^3=\frac{4312}{3}$

$\pi r^3=\frac{4312}{4}$

$r^3=1078\times \frac{7}{22}$

$r=\sqrt[3]{3343}$

$r=7$

Now, Change in radius

$R-r=10.5-7=3.5cm$

Hence, this is the answer.