Question : The curved surface area and the volume of a cylindrical object are 88 cm2 and 132 cm3, respectively. The height (in cm) of the cylindrical object is: (Take $\pi=\frac{22}{7}$ )
Option 1: $4 \frac{2}{3}$
Option 2: $4$
Option 3: $6$
Option 4: $3 \frac{2}{3}$
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Correct Answer: $4 \frac{2}{3}$
Solution :
According to the question
$\frac{\text{Curved surface area of the cylinder}}{\text{Volume of the Cylinder}}$ = $\frac{88}{132}$
⇒ $\frac{2\pi rh}{\pi r^2h }$ = $\frac{88}{132}$ = $\frac{2}{3}$
⇒ $\frac{2}{r}$ = $\frac{2}{3}$
⇒ $r$ = 3 cm
The curved surface area of the cylinder = $2\pi rh$
⇒ 2 × $\frac{22}{7}$ × 3 × $h$ = 88
⇒ $h$ = 4$\frac{2}{3}$ cm
Hence, the correct answer is 4$\frac{2}{3}$.
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