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: $$\left( {{\text{Take }}\pi = \frac{{22}}{7}} \right)$$

Solution (By Examveda Team)

Curved surface area = $$\frac{1}{3}$$ × total surface area
2πrh = $$\frac{1}{3}$$ × [2πrh + 2πr²]
6πrh = 2πrh + 2πr²
4πrh = 2πr²
4h = 2r
h : r = 1x : 2x
Volume of cylinder = πr²h = 4312
$$\frac{{22}}{7}$$ × (2x)² × x = 4312
$$\frac{{22}}{7}$$ × 4x³ = 4312
x³ = 49 × 7
x = 7
Curved surface area = 2πrh
= 2 × $$\frac{{22}}{7}$$ × (2 × 7) × 7
= 22 × 28
= 616 cm²