Question : If the curved surface area of a cylinder is $126\pi$ cm2 and its height is 14 cm, what is the volume of the cylinder?
Option 1: $283 \frac{1}{2} \pi\ \mathrm{cm}^3$
Option 2: $137\frac{1}{2} \pi\ \mathrm{cm}^3$
Option 3: $128\frac{1}{2} \pi\ \mathrm{cm}^3$
Option 4: $125\frac{1}{2} \pi\ \mathrm{cm}^3$
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Correct Answer: $283 \frac{1}{2} \pi\ \mathrm{cm}^3$
Solution :
Let the radius of the cylinder be $r\ \text{cm}$.
Height, $h$ = 14 cm
Curved surface area of a cylinder $ = 126\pi\ \text{cm}^2$
⇒ $2\pi r h=126\pi$
⇒ $2\pi r×14=126\pi$
⇒ $r=\frac{126}{28}=\frac{63}{14}$
The volume of a cylinder = $\pi r^2h=\pi (\frac{63}{14})^2×14=\pi×\frac{63×9}{2}=283 \frac{1}{2} \pi\ \mathrm{cm}^3$
Hence, the correct answer is $283 \frac{1}{2} \pi\ \mathrm{cm}^3$.
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