Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: 2007 · Marks: · Difficulty:
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?
(a)$336 \mathrm{cm}^{2}$
(b)$616 \mathrm{cm}^{2}$
(c)$1232 \mathrm{cm}^{2}$
(d)Cannot be determined
(e)None of these
Answer
Answer (as printed): B
Explanation
Volume of cylinder $=25.872$ litres $=(25.872 \times 1000) \mathrm{cm}^{3}$ $$=25872 \mathrm{cm}^{3} .$$ Let the radius of the base of the cylinder be $r \mathrm{cm}$. Then, height $=(3 r) \mathrm{cm}$. $$\begin{aligned} \therefore \frac{22}{7} \times r^{2} \times(3 r)=25872 \Rightarrow r^{3}=\frac{25872 \times 7}{66} & =2744 \\ \Rightarrow r & =\sqrt[3]{2744}=14 . \end{aligned}$$ Hence, area of the base $=\pi r^{2}=\left(\frac{22}{7} \times 14 \times 14\right) \mathrm{cm}^{2}=616 \mathrm{cm}^{2}$.