Question:
Note Take $\pi=\frac{22}{7}$, unless stated otherwise.
Find the volume of a sphere whose surface area is 154 cm2.
Solution:
Let the radius of the sphere be r cm.
Surface area of the sphere = 154 cm2
$\therefore 4 \pi r^{2}=154$
$\Rightarrow 4 \times \frac{22}{7} \times r^{2}=154$
$\Rightarrow r=\sqrt{\frac{154 \times 7}{4 \times 22}}=\sqrt{12.25}$
$\Rightarrow r=3.5 \mathrm{~cm}$
$\therefore$ Volume of the sphere $=\frac{4}{3} \pi r^{3}=\frac{4}{3} \times \frac{22}{7} \times(3.5)^{3} \approx 179.67 \mathrm{~m}^{3}$
Thus, the volume of the sphere is approximately 179.67 m3.