# Question #90473

Apr 18, 2017

$13500 c {m}^{3}$

#### Explanation:

$\pi = 3 \text{ for this question}$

$\text{surface area of a sphere } = 4 \pi {r}^{2}$

$\therefore 4 \pi {r}^{2} = 2700$

$4 \times \cancel{3} \times {r}^{2} = {\cancel{2700}}^{900}$

${r}^{2} = \frac{900}{4}$

$r = \sqrt{\frac{900}{4}} = \frac{30}{2} = 15 c m$

$\text{volume of sphere } = \frac{4}{3} \pi {r}^{3}$

$V = \frac{4}{\cancel{3}} \times \cancel{3} \times {15}^{3}$

$V = 4 \times 15 \times 15 \times 15 = 13500 c {m}^{3}$

Apr 18, 2017

$13500 c {m}^{3}$

#### Explanation:

Surface are of a sphere ( the globe in this case) is given by:-
$\textcolor{red}{S = 4 \cdot \pi \cdot {r}^{2}}$ where $r$ is radius of sphere.

The volume of a sphere is given by:-
$\textcolor{red}{V = \frac{4}{3} \cdot \pi \cdot {r}^{3}}$ where $r$ is the radius of sphere.

Given that $\pi = 3$.

Surface area is $2700 c {m}^{2}$.
$\therefore$ $4 \cdot \pi \cdot {r}^{2} = 2700$
$\implies 4 \cdot 3 \cdot {r}^{2} = 2700$
$\implies {r}^{2} = \frac{2700}{3 \cdot 4} = \frac{900}{4}$
$\implies r = \sqrt{\frac{900}{4}} = \frac{30}{2} = 15 c m$.

Method 1.
Now volume is $\frac{4}{3} \cdot \pi \cdot {r}^{3}$
$\therefore$ $V = \frac{4}{3} \cdot 3 \cdot {15}^{3} = 4 \cdot 3375 = 13500 c {m}^{3}$

Method 2.
$S = 4 \cdot \pi \cdot {r}^{2}$ ------------------(1.)
$V = \frac{4}{3} \cdot \pi \cdot {r}^{3}$ ------------------(2.)

Dividing equations (1.) & (2.)
$\frac{S}{V} = \frac{4 \cdot \cancel{\pi} \cdot {r}^{2}}{\frac{4}{3} \cdot \cancel{\pi} \cdot {r}^{3}} = \frac{3}{r}$

$\implies \frac{S}{V} = \frac{3}{r}$

$\implies V = \frac{S \cdot r}{3} = \frac{2700 \cdot 15}{3} = 13500 c {m}^{3}$