Question:
If the surface area of a sphere is (144π) m2, then its volume is
(a) $(288 \pi) \mathrm{m}^{3}$
(b) $(188 \pi) \mathrm{m}^{3}$
(c) $(300 \pi) \mathrm{m}^{3}$
(d) $(316 \pi) \mathrm{m}^{3}$
Solution:
(a) $(288 \pi) \mathrm{m}^{3}$
Surface area $=(144 \pi) \mathrm{m}^{2}$
Ler r m be the radius of the sphere.
Then we have:
$4 \pi r^{2}=144 \pi$
$\Rightarrow r^{2}=\frac{144}{4}=36$
$\Rightarrow r=6 \mathrm{~m}$
$\therefore$ Volume of the sphere $=\frac{4}{3} \pi r^{3}$
$=\frac{4}{3} \pi \times 6 \times 6 \times 6$
$=288 \pi \mathrm{m}^{3}$