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: A
Explanation
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 3 Vol. of water = 16\(\pi\) - \(\frac{4 \pi}{3}\) = \(\frac{48 - 4 \pi}{3}\) = \(\frac{44 \pi}{3}\)cm3
