Volume Of A Combination Of Solids

 

The volume of the solid formed by joining two basic solids will actually be the sum of the volumes of the constituents, as we see in the examples below.

Example:

Karna runs an industry in a shed which is in the shape of a cuboid surmounted by a half cylinder (see Fig. below). 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 m3 , and there are 20 workers, each of whom occupy about 0.08 m3 space on an average. Then, how much air is in the shed? (Take π = 22/ 7 )

The volume of air inside the shed is given by the volume of air inside the cuboid and inside the half cylinder, taken together. Now, the length, breadth and height of the cuboid are 15 m, 7 m and 8 m, respectively.

Also, the diameter of the half cylinder is 7 m and its height is 15 m.

So, the required volume = volume of the cuboid + 1/ 2 volume of the cylinder

=[ 15*7*8+ (1/2)*(22/7)*(7/2)*(7/2)*15] m^3

=1128.75 m^3

Next, the total space occupied by the machinery = 300 m^3

And the total space occupied by the workers = 20 × 0.08 m^3 = 1.6 m^3

Therefore, the volume of the air, when there are machinery and workers.

=1128.75 – (300.00 + 1.60) = 827.15 m^3