Question:
The surface area of a sphere is 1386 cm2. Its volume is
(a) 1617 cm3
(b) 3234 cm3
(c) 4851 cm3
(d) 9702 cm3
Solution:
(c) $4851 \mathrm{~cm}^{3}$
Surface area $=1386 \mathrm{~cm}^{2}$
Let r cm be the radius of the sphere.
Then we have:
$4 \pi r^{2}=1386$
$\Rightarrow r^{2}=\frac{1386 \times 7}{4 \times 22}=110.25$
$\Rightarrow r=10.5 \mathrm{~cm}$
$\therefore$ Volume of the sphere $=\frac{4}{3} \pi r^{3}$
$=\frac{4}{3} \times \frac{22}{7} \times 10.5 \times 10.5 \times 10.5$
$=4851 \mathrm{~cm}^{3}$