Example 5 : Shanta runs an industry in
a shed which is in the shape of a cuboid
surmounted by a half cylinder (see Fig.
13.12). If the base of the shed is of
dimension 7 mx 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 m², and
there are 20 workers, each of whom
occupy about 0.08 m space on an
average. Then, how much air is in the
22
shed? (Take it
)
7
Answers
Answer:
827.15 m cube
Step-by-step explanation:
Clearly, the volume of air inside the shed (when there is no people or machinary) is equal to the volume of air inside the cuboid and inside the half-cylinder taken together
For cuboidal part, we have
Length =15m; breadth =7m and height =8m
Volume of cuboidal part =15×7×8m
2
=840m
3
Clearly
Radius =r=
2
7
m
Height (length) of half-cylinder=h= Length of cuboid=15m
Volume of half cylinder
=
2
1
πr
2
h=
2
1
×
7
22
×(
2
7
)
2
×15m
3
=288.75m
3
Volume of air inside the shed when there is no people or machinary
=(840+288.75)m
3
=1128.75m
3
Total space occupied by 20 workers =20×0.08m
3
=1.6m
3
Total space occupied by the machinery =300m
3
Volume of the air inside the shed when there are machine and workers inside it
=(1128.75−1.6−300)m
3
=827.15m
3
please mark me brainliest