Question : The volume of a sphere is given by 130977 cm3. Its surface area (in cm2) is:
Option 1: 16847
Option 2: 12474
Option 3: 17424
Option 4: 14274
Correct Answer: 12474
Solution :
Volume of a sphere = $(\frac{4}{3}) × \pi r^3$, where $r$ is the radius of the sphere.
⇒ $(\frac{4}{3}) × (\frac{22}{7}) × r^3 = 130977$
⇒ $r^3 = \frac{(130977 × 7 × 3)}{ (4 × 22)}$
⇒ $r = \sqrt[3]{\frac{3×3×3×3×3×3×7×7×7×11}{2 × 2 × 2×11}}$
$\therefore r = \frac{63}{2}$
So, the surface area of the sphere $=4 \pi r^2 = 4 × (\frac{22}{7}) × (\frac{63}{2}) × (\frac{63}{2})=$ 12474 cm
2
Hence, the correct answer is 12474.
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