A steel ball of radius 1 cm is dropped into a cylinder of radius 2cm and height 4cm. If the cylinder is now filled with water, what is the volume of the water in the cylinder?
-
A.
(frac{44}{3})(pi)cm3 -
B.
12(pi)cm3 -
C.
(frac{38}{3})(pi)cm3 -
D.
(frac{40}{3})(pi)cm3 -
E.
(frac{32}{33})(pi)cm3
Correct Answer: Option A
Explanation
Volume of steel ball = (frac{4pi r^2}{3})
= (frac{4}{3}) (pi) x 1
= (frac{4 pi}{3})cm3
Vol. of cylinder = (pi)r2h
= (pi) x 22 x 3
Vol. of water = 16(pi) – (frac{4 pi}{3})
= (frac{48 – 4 pi}{3})
= (frac{44 pi}{3})cm3