Question : The volume of a solid right circular cylinder of height 8 cm is $392 \pi$ cm3. Its curved surface area (in cm2) is:
Option 1: $161 \pi$
Option 2: $96 \pi$
Option 3: $210 \pi$
Option 4: $112 \pi$
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Correct Answer: $112 \pi$
Solution :
The volume $V$ of a right circular cylinder is given by the formula $V = \pi r^2 h$, where $r$ is the radius and $h$ is the height.
Given that $V = 392\pi \;\text{cm}^3$ and $h = 8 \;\text{cm}$.
$⇒392\pi = \pi r^2 \times 8$
$⇒r^2 = \frac{392}{8} = 49$
$⇒r = \sqrt{49} = 7 \;\text{cm}$
The curved surface area $A$ of a right circular cylinder.
$A = 2\pi rh$
Substituting $r = 7 \;\text{cm}$ and $h = 8 \;\text{cm}$.
$\therefore A = 2\pi \times 7 \times 8 = 112\pi \;\text{cm}^2$
Hence, the correct answer is $112\pi$.
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