Question : If the volume of a sphere is $179 \frac{2}{3}$ m3, what is its surface area?
Option 1: 221 m2
Option 2: 154 m2
Option 3: 144 m2
Option 4: 151 m2
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Correct Answer: 154 m 2
Solution :
Given, the volume of a sphere is $179 \frac{2}{3} = \frac{539}{3}$
Volume of a sphere with radius, $r$ = $\frac{4}{3}\pi r^3$
⇒ $\frac{4}{3}\pi r^3=\frac{539}{3}$
⇒ $\frac{4}{3}\times \frac{22}{7}\times r^3=\frac{539}{3}$
⇒ $r^3=\frac{49\times 7}{4\times 2}$
$\therefore r=\frac{7}{2}$ m
Surface area = $4\pi r^2$
= $4\times \frac{22}{7}\times \frac{49}{4}$
= $154$ m
2
Hence, the correct answer is 154 m
2
.
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