Question : If the surface area of a sphere is $1386 \mathrm{~cm}^2$, then its volume is:
(Take $\pi=\frac{22}{7}$ )
Option 1: 8451 cm3
Option 2: 4851 cm3
Option 3: 5418 cm3
Option 4: 4581 cm3
Correct Answer: 4851 cm 3
Solution :
The surface area of the sphere = 1386 cm$^2$
Surface area of a sphere = $4\pi r^2$
⇒ $4\pi r^2$ = 1386
⇒ $4 × (\frac{22}{7}) × r^2$ = 1386
⇒ $r = \frac{21}{2}$ cm
Volume of a sphere = $(\frac{4}{3})\pi r^3$
= $(\frac{4}{3}) × (\frac{22}{7}) × (\frac{21}{2})^3 $
= 4851 cm$^3$
$\therefore$ The volume of the sphere is 4851 cm$^3$.
Hence, the correct answer is 4851 cm
3
.
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