Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: 2006 · Marks: · Difficulty:
The ratio of the volumes of a right circular cylinder and a sphere is 3 : 2. If the radius of the sphere is double the radius of the base of the cylinder, find the ratio of the total surface areas of the cylinder and the sphere.
(a)9 : 8
(b)13 : 8
(c)15 : 8
(d)17 : 8
Answer
Answer (as printed): D
Explanation
Let the radius of the cylinder be $r$. Then, radius of the sphere $=2 r$. $$\begin{aligned} & \frac{\text { Volume of cylinder }}{\text { Volume of sphere }}=\frac{3}{2} \Rightarrow \frac{\pi r^{2} h}{\frac{4}{3} \pi(2 r)^{3}}=\frac{3}{2} \Rightarrow \frac{h}{r}=16 \Rightarrow h \\ & \begin{aligned} \therefore \text { Required ratio } & =\frac{\text { Total suface area of cylinder }}{\text { surface area of sphere }} \\ & =\frac{2 \pi r \cdot(16 r)+2 \pi r^{2}}{4 \pi(2 r)^{2}}=\frac{34 \pi r^{2}}{16 \pi r^{2}}=\frac{17}{8} . \end{aligned} \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.