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 ?

Solution(By Examveda Team)

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