Question

A hollow spherical ball whose inner radius is $4cm$ is full of water. Half of the water is transferred to a conical cup and it completely filled the cup. If the height of the cup is $2cm$, then the radius of the base of cone, in $cm$ is:

• A. $4cm$
• B. $8\pi cm$
• C. $8cm$
• D. $16cm$

Answer 1

The correct option is C $8cm$

As half of the water in the spherical cup is transferred to the conical cup, half of the volume of water in the spherical cup is equal to the volume of water in the conical cup up to $2cm$.

Volume of a cone $=\frac{1}{3}\pi r^{2}h$ where r is the radius of the base of the cone and h is the height.

Volume of a sphere of radius ${}^{\prime }{r}^{\prime }$ $=\frac{4}{3}\pi r^3$

Hence, $\frac{1}{2}\times$ (Volume of sphere) $=$ Volume of the cone

$\therefore \frac{1}{2}\times \frac{4}{3}\pi \times 4^3=\frac{1}{3}\pi r^2\times 2$

$\therefore r^2=64$

$\therefore r=8cm$