A toy is in the shape of a cone mounted on a hemisphere of same base radius. If the volume of the toy is 231 cm3 and its diameter is 7 cm, find the height of the toy.
A toy is in the shape of a cone mounted on a hemisphere of same base radius.
Volume of Toy = 231 cm3
Base Diameter of toy = 7 cm
Base radius of toy = 7/2 cm = 3.5 cm
Volume of hemisphere = 2/3 πr3
= 2/3 × 22/7 × 3.53 cm3
= 89.83 cm3
Volume of cone = Volume of hemisphere – Volume of toy
= 231 – 89.83 cm3 = 141.17 cm3
Volume of cone is given by 1/3 πr2h
Where h is the height of cone
∴ 1/3 × πr2h = 141.17 cm3
⇒ 1/3 × 22/7 × 3.5 × 3.5 × h = 141.17 cm3
⇒ h = 141.17 × 3 × 7/22 × 1/3.5 × 1/3.5
⇒ h = 11 cm
Height of cone = 11 cm
Height of toy = Height of cone + Height of hemisphere
= 11 cm + 3.5 cm = 14.5 cm
[Height of hemisphere = Radius of hemisphere]
∴ Height of toy is 14.5 cm.