If the surface area of a sphere is (144π) m2,
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 $=\frac{4}{3} \pi r^{3}$

$=\frac{4}{3} \pi \times 6 \times 6 \times 6$

$=288 \pi \mathrm{m}^{3}$