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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