A solid metallic sphere of radius r is converted into a solid right circular cylinder of radius R. If the… · ABC26GN5021
Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: A.A.O. Exam 2010
A solid metallic sphere of radius $r$ is converted into a solid right circular cylinder of radius $R$. If the height of the cylinder is twice the radius of the sphere, then
(a)$R=r$
(b)$R=r \sqrt{\frac{2}{3}}$
(c)$R=\sqrt{\frac{2 r}{3}}$
(d)$R=\frac{2 r}{3}$
Answer
Answer (as printed): B
Explanation
Volume of the sphere = Volume of the cylinder $$\Rightarrow \frac{4}{3} \pi r^{3}=\pi R^{2} \cdot 2 r \Rightarrow 2 r^{2}=3 R^{2} \Rightarrow R^{2}=\frac{2 r^{2}}{3} \Rightarrow R=r \sqrt{\frac{2}{3}} .$$
Explanation as extracted from the printed page; notation may be imperfect.