Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: 2007 · Marks: · Difficulty:
A right circular cylinder and a sphere are of equal volumes and their radii are also equal. If $h$ is the height of the cylinder and $d$, the diameter of the sphere, then
(a)$h=d$
(b)$2 h=d$
(c)$\frac{h}{3}=\frac{d}{2}$
(d)$\frac{h}{2}=\frac{d}{3}$
Answer
Answer (as printed): D
Explanation
Let the radius of the sphere and that of the right circular cylinder be $r$. Then, volume of the cylinder $=\pi r^{2} h$. $$\begin{aligned} & \text { Volume of the sphere }=\frac{4}{3} \pi r^{3} . \\ & \therefore \pi r^{2} h=\frac{4}{3} \pi r^{3} \Rightarrow 3 h=4 r \Rightarrow 3 h=2 d \Rightarrow \frac{h}{2}=\frac{d}{3} . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.