Question

The formula for the volume V of a sphere is given as $V=\frac{4}{3}\pi r^3$.
a) Find V if $r=5cm$.
b) Make r the subject of the formula.
c) Find the radius of a sphere of volume 2500 m³.

Answer 1

a) Volume, $V=\frac{4}{3}\pi r^3$

$=\frac{4}{3}\times \pi \times 5^3$

$=\frac{4}{3}\pi \left(125\right)$

$\therefore V=\frac{500\pi }{3}c{m}^3$
b) As we have $V=\frac{4}{3}\pi r^3$

$\Rightarrow r^3=\frac{3}{4\pi }V$

$\Rightarrow r=\left(\frac{3}{4\pi }V\right){}^{\frac{1}{3}}$

c) Since $V=\frac{4}{3}\pi r^3$

$\Rightarrow 2500=\frac{4}{3}\times \frac{22}{7}\times r^3$

$\Rightarrow r^3=2500\times \frac{3}{4}\times \frac{7}{22}$

$\Rightarrow r^3=625\times 3\times \frac{7}{22}$
$\Rightarrow r^3=596.590$

$\Rightarrow r=\sqrt[3]{3596.590}$

$\therefore r=8.41m$