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: Option C
Explanation
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
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