A steel ball of radius 1 cm is dropped into a cylinder of radius 2cm...

JAMB 1979

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

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Correct Answer: Option 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 4

Vol. of water = 16\(\pi\) - \(\frac{4 \pi}{3}\)

= \(\frac{48 - 4 \pi}{3}\)

= \(\frac{44 \pi}{3}\)cm\(^3\)