Question

If a solid sphere of radius r is melted and cast into the shape of a solid cone of height r, then the radius of the base of the cone is

• A. 2r
• B. 3r
• C. r
• D. 4r

Answer 1

The correct option is A

2r

Radius of a sphere = r

then its volume $=\frac{4}{3}\pi r^3$

$\therefore$ Volume of solid cone $=\frac{4}{3}\pi r^3$

Height (h) = r

$\therefore Radius=\sqrt{\frac{Volume}{\frac{1}{3}\pi h}}$

$=\sqrt{\frac{\frac{4}{3}\pi r^3}{\frac{1}{3}\pi r}}$

$=\sqrt{\frac{4\pi r^3\times 3}{3\pi r}}$

$=\sqrt{4r^2}=2r$