A wooden toy was made by scooping out a hemisphere of same radius from each end of a solid cylinder. If the height of the cylinder is 10 cm and its base is of radius 3.5 cm, find the volume of wood in the toy.
Given height of cylinder = h = 10 cm
Radius of cylinder = r = 3.5 cm
Radius of hemisphere = R = 3.5 cm
Explanation: In this question the volume of wood in toy can be calculated by subtracting the volume of two hemisphere from the volume of cylinder.
So, volume of cylinder = πr2h
Where r = radius of cylinder and h = height of cylinder
⇒ Volume of cylinder = π × (3.5)2 × 10 (from given values)
⇒ Volume of cylinder = π × 12.25 × 10
∴ Volume of cylinder = 122.5π cm3→eqn1
Volume of a hemisphere
(where R is radius of hemisphere)
∴ Volume of two hemisphere
Volume of wood in toy = eqn1 – eqn2
⇒Volume of wood in toy
(taking π common)
∴ Volume of wood in toy = 205.333 cm3
Volume of wood in toy is 205.333 cm3.