. A toy is in the form of a cone mounted on a hemisphere with same radius. The diameter of the base of the conical portion is 7 cm and the total height of the toy is 14.5 cm. Find the volume of the toy.
Answers
CONE:-
diameter = d = 7cm
∴radius = r = d÷2
= 7/2cm = 3.5cm
HEMISPHERE:-
Given that the cone is mounted on a hemisphere,
radius of the cone = radius of the hemisphere
Total height of the toy = 14.5cm
We know that radius of the hemisphere = height of the hemisphere.
∴If we subtract height of hemisphere from the height of the toy, we'll get the height of the cone
(i.e), Height of cone = H
Height of toy = Height of [cone + hemisphere]
14.5 = H + 3.5cm
∴ H = 11
⇒ The height of the cone is 11cm.
Volume of the toy = Volume of cone + Volume of hemisphere
= 1/3πr²H + 2/3πr³
= 1/3πr² (H+2r) [Taking out the common]
= 1 22 7 7 [ 11 + 2 × 3.5 ]
--- × --- × --- × ---
3 7 2 2
= 1 22 1 7 ( 11 + 7)
--- × × ---- × ----
3 2 2
= 1/3 × 11 × 3.5 (18)
= 11 × 63
------------
3
= 693 / 3 = 231cm³
∴The volume of the toy = 231cm³.