Question

The volume of the sphere is $905\frac{1}{7}c{m}^3$. find its radius.

Answer 1

Let the radius of the sphere be $r$.

Now, Volume of Sphere $=905\frac{1}{7}c{m}^3=\frac{6336}{7}c{m}^3$ [Given]

We know that volume of sphere is given by the formula, $V=\frac{4}{3}\pi r^3$

$\therefore \frac{4}{3}\pi r^3=905\frac{1}{7}$

$\Rightarrow \frac{4}{3}\times \frac{22}{7}\times r^3=\frac{6336}{7}$

$\Rightarrow r^3=\frac{6336}{7}\times \frac{7}{22}\times \frac{3}{4}$

$\Rightarrow r^3=\frac{288}{1}\times \frac{1}{1}\times \frac{3}{4}$

$\Rightarrow r^3=72\times 3=216$

$\Rightarrow r=\sqrt[3]{3216}$

$r=\sqrt[3]{36\times 6\times 6}$

$r=6$

Hence, the radius of the given sphere is $6cm.$