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: 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 = \(\frac{1}{8}\) = \(\frac{\pi}{6}\) x \(\frac{1}{4\sqrt{3}}\) = \(\frac{\pi}{24\sqrt{3}}\)
