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{3pi}{24}}) -
C.
(frac{pi}{24sqrt{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
= (frac{1}{8})
= (frac{pi}{6}) x (frac{1}{4sqrt{3}})
= (frac{pi}{24sqrt{3}})