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Combination of Solids

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

 

Example 7. A circus tent is cylindrical to a height of 3m and conical above it. If its base radius is 52.5m and slant height of the conical portion is 53m, find the area of the canvas needed to make the tent.

Solution:- Radius of the cylinder

= Radius of the cone = 52.5m

Height of the cylinder = 3m

Slant height of the cone = 53m

Area of the canvas = curved surface area of cone + curved surface area of cylinder

Example 8. A boiler is in the form of cylinder 2m long with hemispherical ands each of 2m diameter. Find the volume of the boiler.

Solution:- Length of cylindrical portion = h = 2m

Radius of cylinder = Radius of hemisphere

                                 = r = 1m

Volume of boiler = Volume of cylinder + volume of two hemispheres

 

 


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