A hollow right prism of equilateral triangular base of side 4cm is filled with water up to a certain height. If a sphere of radius \(\frac{1}{2}\)cm is immersed in the water, then the rise of water is

A.

1cm

B.

\(\sqrt{\frac{3\pi}{24}}\)

C.

\(\frac{\pi}{24\sqrt{3}}\)

D.

24\(\sqrt{3}\)

Correct answer is C

The rise of water is equivalent to the volume of the sphere of radius \(\frac{1}{2}\)cm immersed x \(\frac{1}{\text{No. of sides sq. root 3}}\)

Vol. of sphere of radius = 4\(\pi\) x \(\frac{1}{8}\) x \(\frac{1}{3}\) - (\(\frac{1}{2}\))3

= \(\frac{1}{8}\)

= \(\frac{\pi}{6}\) x \(\frac{1}{4\sqrt{3}}\)

= \(\frac{\pi}{24\sqrt{3}}\)