Question 2
Selvi s house has an overhead tank in the shape of a cylinder. This is filled by pumping water from a sump (an underground tank) which is in the shape of a cuboid. The sump has dimensions 1.57 m 1.44 m 95cm. The overhead tank has its radius 60 cm and height 95 cm. Find the height of the water left in the sump after the overhead tank has been completely filled with water from the sump which had been full. Compare the capacity of the tank with that of the sump. (Use = 3.14)
Lets first find volume of water left in sump
Volume of water left in the cuboidal sump after filling the tank
= Volume of cuboidal sump Volume of cylindrical tank
Volume of cuboidal sump
Length (l) = 1.57 m
Breadth (b) = 1.44 m
Height (h) = 95 cm = 95 1/100 m = 0.95 m
Volume of sump = Length Breadth Height
= lbh
= 1.57 1.44 95
= 2.147 m3
Volume of overhead tank
Height of overhead tank = h = 95 cm = 95 1/100 m = 0.95 m
And, radius = r = 60 cm= 60 1/100 m = 0.6 m
Volume of overhead tank = 2
= (0.6)2 (0.95)
= 0.342 m3
= 0.342 3.14
= 1.074 m3
Volume of water left in the cuboidal sump after filling the tank
= Volume of cuboidal sump Volume of cylindrical tank
= 2.147 1.073
= 1.073 m3
Now,
Volume of water left in cuboidal sump = 1.073
Length Breadth Height = 1.73
1.57 1.44 h = 1.073
h = 1.073/(1.57 1.44)
h = 0.475 m
h = 0.475 100 cm
h = 47.5 cm
So, height of water left in sump = 47.5 cm
Also,
( )/( ) = ( )/( )
= 1.073/2.147
= 0.499
= 0.5 (approximately)
= 5/10
= 1/2
Hence, capacity of the tank is half the capacity of the sump .

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo

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