Question : The total surface area of a cylinder is 4092 cm2 and the diameter of its base is 21 cm. What is 50% volume (in cm3) of the cylinder (nearest to an integer)?
Option 1: 8832
Option 2: 8822
Option 3: 8922
Option 4: 8932
Correct Answer: 8922
Solution :
The diameter of the base = 21
The radius of the base, $r$ = $\frac{21}{2}$
Let $h$ be the height.
According to the question,
Total surface area of cylinder = $2\pi r(r + h)$
⇒ $2 \times \frac{22}{7} \times \frac{21}{2}(\frac{21}{2} + h) = 4092$
⇒ $\frac{21}{2} + h = 62$
⇒ $h = 62 – \frac{21}{2}$
⇒ $h = \frac{124-21}{2}$
⇒ $h = \frac{103}{2}$
Now,
Volume of the cylinder = $\pi r^2h=\frac{22}{7} \times \frac{21}{2} \times \frac{21}{2} \times \frac{103}{2}=\frac{71379}{4}\ \text{cm}^3$
50% volume of the cylinder = $\frac{1}{2} × \frac{71379}{4}=8922\ \text{cm}^3$
Hence, the correct answer is 8922.
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