Question : The volume of a cylinder is 4312 cm3. Its curved surface area is one-third of its total surface area. Its curved surface area (in cm2) is:
(Take $\pi=\frac{22}{7}$ )
Option 1: 572 cm2
Option 2: 528 cm2
Option 3: 660 cm2
Option 4: 616 cm2
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Correct Answer: 616 cm 2
Solution :
According to the question,
Curved surface area = $\frac{\text{Total surface area}}{3}$
⇒ $2\pi rh = \frac{2\pi r(h + r)}{3}$
⇒ $3h = (h + r)$
⇒ $2h = r$
Now,
The volume of a cylinder = 4312 cm
3
⇒ $\pi r^2h = 4312$
⇒ $\frac{22}{7}\times r^2\times \frac{r}{2} = 4312$
⇒ $r^3 = 14^3$
⇒ $r = 14$
So, $h = \frac{r}{2} = \frac{14}{2} = 7$
Now, Curved Surface Area = $2\pi rh$
= $2 \times \frac{22}{7} \times 14 \times 7$
= $616$ cm
2
Hence, the correct answer is 616 cm
2
.
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