The curved surface area of a right cylinder is 3696 cm². Its height is three times its radius. What is the capacity (in liters) of the cylinder? $$\left( {{\text{Take }}\pi = \frac{{22}}{7}} \right)$$

Solution (By Examveda Team)

$$\eqalign{ & r:h = 1:3 \cr & 2\pi rh = 3696 \cr & 2 \times \frac{{22}}{7} \times x \times 3x = 3696 \cr & 3{x^2} = \frac{{3696 \times 7}}{{44}} \cr & {x^2} = \frac{{1232 \times 7}}{{44}} \cr & {x^2} = \frac{{112 \times 7}}{4} \cr & {x^2} = 28 \times 7 \cr & x = 14 \cr & {\text{Volume}} = \pi {r^2}h \cr & = \frac{{22}}{7} \times {14^2} \times 42 \cr & = \frac{{22}}{7} \times 14 \times 14 \times 42 \cr & = 25872{\text{ c}}{{\text{m}}^3} \cr & = 25.872{\text{ L}} \cr} $$