Question

If the height of the cone is half the radius of the sphere, then the radius of the base of a cone which has the same volume as a sphere of $5$ cm radius, is

• A. $10$ cm
• B. $10\sqrt{2}$ cm
• C. $\frac{5\sqrt{2}}{2}$ cm
• D. $\frac{10\sqrt{3}}{3}$ cm

Answer 1

Answer: (B)

$10\sqrt{2}$ cm

Volume of the sphere$=\frac{4}{3}\pi {.5}^3=\frac{500}{3}\pi$
Volume of the cone $=\frac{1}{3}\pi r^2.\frac{5}{2}=\frac{5}{6}\pi r^2$
$\therefore \frac{5}{6}\pi r^2=\frac{500}{3}\pi \Rightarrow r=10\sqrt{2}$