Question : The volume of a solid sphere is $4500 \pi \;cm^3$. The surface area of the solid sphere is:
Option 1: $700 \pi\; \text{cm}^2$
Option 2: $850 \pi\; \text{cm}^2$
Option 3: $900 \pi\; \text{cm}^2$
Option 4: $810 \pi\; \text{cm}^2$
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Correct Answer: $900 \pi\; \text{cm}^2$
Solution :
Volume of a solid sphere = $4500 \pi$ cm$^3$
$⇒\frac{4}{3}×\pi×r^3$ = $4500 \pi$ cm$^3$
$⇒r^3$ = $\frac{4500×3}{4}$ = 3375
$\therefore r$ = 15 cm
The Surface area of the solid sphere = $4\pi r^2$
= 4 × $\pi$ × 15$^2$ cm$^2$
= 900$ \pi$ cm$^2$
Hence, the correct answer is $900 \pi\; \text{cm}^2$.
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