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
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
Volume of steel ball = \(\frac{4\pi r^2}{3}\)
= \(\frac{4}{3}\) \(\pi\) x 1
= \(\frac{4 \pi}{3}\)cm3
Vol. of cylinder = \(\pi\)r2h
= \(\pi\) x 22 x 4
Vol. of water = 16\(\pi\) - \(\frac{4 \pi}{3}\)
= \(\frac{48 - 4 \pi}{3}\)
= \(\frac{44 \pi}{3}\)cm\(^3\)
Source: Myschool Past Questions Archive (Record #32659)