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Volume of a Combination of Solids

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In the previous section, we have discussed how to find the surface area of solids made up of a combination of two basic solids. Here, we shall see how to calculate their volumes.

Volume of combination can be found out by adding volumes of different solids or by subtracting volumes of different solids.

Example 1- Shanta runs an industry in a shed which is in the shape of a cuboid surmounted by a half cylinder. If the base of the shed is of dimension 7 m × 15 m, and the height of the cuboidal portion is 8 m, find the volume of air that the shed can hold. Further, suppose the machinery in the shed occupies a total space of `300 m^3`, and there are 20 workers, each of whom occupy about `0.08 m^3` space on an average. Then, how much air is in the shed? `(Take   pi= 22/7)`

Solution- Volume of air in shed= Volume of shed- Space occupied by workers and machinery

Volume of shed= Volume of cuboid+ Volume of half cylinder


`= (8 xx 7 xx 15)+ 1/2  pi r^2h`


= `(8 xx 7 xx 15)+ 1/2 xx 22/7 xx (7/2)^2 xx 15`


Volume of shed =`1128.75 cm^3`


Volume of air in shed= Volume of shed- Space occupied by workers and machinery


`= 1128.75- 300+ (20 xx 0.08)`


Volume of air in shed= `827.15 m^3`


Example 2- A juice seller was serving his customers using glasses. The inner diameter of the cylindrical glass was 5 cm, but the bottom of the glass had a hemispherical raised portion which reduced the capacity of the glass. If the height of a glass was 10 cm, find the apparent capacity of the glass and its actual capacity. (Use π = 3.14.)

Solution: Capacity of the glass= Volume of glass- Volume of hemisphere

= `pi r^2h -2/3 pi r^3`

= `[3.14 (2.5)^2  xx 10] -[2/3 xx  3.14 xx (2.5)^3]`

`"Capacity of the glass"= 163.54 cm^3`

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