Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: · Marks: · Difficulty:
The radius of a cylinder is 5m more than its height. If the curved surface area of the cylinder is $792 \mathrm{m}^{2}$, what is the volume of the cylinder? (in $\mathrm{m}^{3}$ ) [IBPS-Bank Spl. Officers (IT) Exam, 2015]
(a)5712
(b)5244
(c)5544
(d)5306
(e)5462
Answer
Answer (as printed): C
Explanation
Let the height of the cylinder be $x$ m. Then, radius $=(x+5) \mathrm{m}$ Curved surface area of the cylinder $=2 \pi \mathrm{rh}$ Now, $2 \pi(x+5) \times x=792$ $$\begin{aligned} & 2 \times \frac{22}{7} \times\left(x^{2}+5 x\right)=792 \\ & x^{2}+5 x=\frac{792 \times 7}{44}=126 \\ & \Rightarrow x^{2}+5 x=126 \\ & x^{2}+5 x-126=0 \\ & x^{2}+14 x-9 x-126=0 \\ & x(x+14)-9(x+14)=0 \\ & (x-9)(x+14)=0 \end{aligned}$$ $\therefore x=9,-14$ (neglect negative value) ∴ Height of cylinder $=9 \mathrm{m}$ ∴ Radius of cylinder $=9+5=14 \mathrm{m}$ Volume of cylinder $=\pi r^{2} h$ $$=\frac{22}{7} \times 14 \times 14 \times 9=5544 \mathrm{m}^{3}$$