Capacity of a cylindrical vessel is 25.872 litres. If the height of the cylinder is three times the radius of its base, what is the area of the base ?

Answer: Option B

Volume of cylinder :
$$\begin{array}{rl}& =25.872\text{litres}\\ & =\left(25.872\times 1000\right)\text{c}{\text{m}}^{\text{3}}\\ & =25872\text{ c}{\text{m}}^3\end{array}$$
Let the radius of the base of the cylinder be r cm
Then, height = (3r) cm
$$\begin{array}{rl}& \therefore \frac{22}{7}\times r^2\times \left(3r\right)=25872\\ & \Rightarrow r^3=\frac{25872\times 7}{66}\\ & \Rightarrow r^3=2744\\ & \Rightarrow r=\text{root}3\text{of}2744\\ & \Rightarrow r=14\end{array}$$
Hence, area of the base :
$$\begin{array}{rl}& =\pi r^2\\ & =\left(\frac{22}{7}\times 14\times 14\right)\text{ c}{\text{m}}^2\\ & =616\text{ c}{\text{m}}^2\end{array}$$