JAMB Mathematics 1979 Question 20

Question 20

Mensuration of Solids

A steel ball of radius 1cm 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.⁴⁴/₃πcm³
B.12πcm³
C.²⁵/₃πcm³
D.⁴³/₃πcm³
E.³²/₃πcm³

Show the answer and explanation

Answer: A (⁴⁴/₃πcm³)

Explanation

The cylinder holds π × 2² × 4 = 16π cm³. The ball takes up (4/3)π × 1³, leaving 16π − 4π/3 = 44π/3 cm³ for water.