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

1cm

$\sqrt{\frac{3\pi}{24}}$

$\frac{\pi}{24\sqrt{3}}$

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 $\frac{1}{4\sqrt{3}}$

= $\frac{\pi}{24\sqrt{3}}$

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