From a solid cylinder of height 14 cm and base diameter 7 cm, two equal conical holes each of radius 2.1 cm and height 4 cm are cut off. Find the volume of the remaining solid.
Height of solid cylinder = h = 14 cm
Diameter of solid cylinder = 7 cm
Radius of solid cylinder = r = Diameter ÷ 2 = 7/2 cm = 3.5 cm
Volume of solid cylinder = πr2h
= 22/7 × 3.5 × 3.5 × 14 cm3
= 539 cm3
Height of conical cavity = h’ = 4 cm
Radius conical cavity = r’ = 2.1 cm
Volume of conical cavity = 1/3 πr’2h’
= 1/3 × 22/7 × 2.1 × 2.1 × 4 cm3
= 18.48 cm3
Since, there are two conical cavities
∴ Volume of two conical cavities = 2 × 18.48 cm3 = 36.96 cm3
Volume of remaining solid = Volume of solid cylinder – Volume of two conical cavity
Volume of remaining solid = 539 cm3 – 36.96 cm3
= 502.04 cm3