Question : If the volume of a sphere is 4851 cm3, then its surface area (in cm2)is: $\left(\right.$Take $\pi=\frac{22}{7})$
Option 1: 1427
Option 2: 1386
Option 3: 1399
Option 4: 1268
Correct Answer: 1386
Solution :
Given:
The volume of the sphere of radius $r$ = 4851 cm
3
We know,
Volume of the sphere $=\frac{4}{3} ×\pi r^3$
⇒ $4851 = \frac{4}{3} × \frac{22}{7} × r^3$
⇒ $r^3= 4851 × \frac{21}{88}$
⇒ $r^3= 441 × \frac{21}{8}$
⇒ $r = \frac{21}{2}$
Also, Surface area of sphere = $4 × \pi r^2$
= $4 × \frac{22}{7} × (\frac{21}{2})^2$
= $4 × \frac{22}{7} × \frac{441}{4}$
= $22 × 63$
= $1386$ cm
2
Hence, the correct answer is 1386 cm
2
.
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