Chapter 14 - Mensuration

Combination of Solids

In our day-today life wer come across different solids which are combination of two or more solids. For example, top is a combination of a hemisphere and cone, circus tent is a combination of cone and cylinder. In this section we shall deal with such types of solid and find their surface area and volume.

Example 6. A solid toy is in the form of a hemisphere surmounted by a right circular cone. If height of the cone is 4cm and diameter of the base is 6cm, Calculate:

1. The volume of the toy
2. The surface area of the toy.

Solution:- Radius, r of cone = 6/2 = 3cm

Height, h of cone = 4cm

Radius, r of hemisphere = 3cm

Slant height

(i) Volume of the toy = volume of cone + volume of hemisphere

(ii) Surface area of the toy = Curve surface area of cone + curved surface area of hemisphere

= 3.14 X 3 X (5 + 2 X 3)

= 103.62cm²