Suman house has an overhead tank which is cylindrical in shape. It's radius is 50 cm and height 91 cm this tank is filled by pumping water from a sump(an underground tank) which is cuboidal in shape. The dimensions of sump are 1.5 m ×1 m×95 cm. An overflow pipe of the tank is connected to the sump to avoid any loss of water due to overflow (a) find the height of water left in the sump after the overhead tank has been completely filled with water from the sump which had been full
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The answer of this question is 50cm×91cm×95cm = 432250
Golda:
Wrong answer.
No this is the right
You have not explained in detail. You are taking length and breadth of the overhead tank and considering the height of the sump, then how is it possible to have this answer.
Length and breadth of the sump (underground tank) will not change. Only height will change because of the decrease in the water level.
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Solution:-
Radius of the cylindrical tank = 50 cm
Height of the cylindrical tank = 91 cm
Volume of the cylindrical overhead tank = πr²h
⇒ 22/7*50*50*91
⇒ 715000 cm³
Length of the cuboidal tank = 1.5 m = 150 cm
Breadth of the cuboidal tank = 1 m = 100 cm
Height of the cuboidal tank = 95 cm
Volume of the cuboidal tank = L*B*H
⇒ 150*100*95
⇒ 1425000 cm³
When the overhead tank is completely filled by the water from the sump, the volume of the remaining water in the sump = Volume of the cuboidal tank - volume of the cylindrical tank
⇒ 1425000 - 715000
= 710000 cm³
Let H₁ be the height of water that is left in the sump.
Length and breadth will remain the same for the sump because only the height of water will decrease due to decrease in water level.
Volume of water remained in the sump = L*B*H₁
⇒ 710000 = 150*100*H₁
⇒ H₁ = 710000/15000
⇒ H₁ = 47.33 cm
So, height of the water left in the sump is 47.33 cm
Answer.
Radius of the cylindrical tank = 50 cm
Height of the cylindrical tank = 91 cm
Volume of the cylindrical overhead tank = πr²h
⇒ 22/7*50*50*91
⇒ 715000 cm³
Length of the cuboidal tank = 1.5 m = 150 cm
Breadth of the cuboidal tank = 1 m = 100 cm
Height of the cuboidal tank = 95 cm
Volume of the cuboidal tank = L*B*H
⇒ 150*100*95
⇒ 1425000 cm³
When the overhead tank is completely filled by the water from the sump, the volume of the remaining water in the sump = Volume of the cuboidal tank - volume of the cylindrical tank
⇒ 1425000 - 715000
= 710000 cm³
Let H₁ be the height of water that is left in the sump.
Length and breadth will remain the same for the sump because only the height of water will decrease due to decrease in water level.
Volume of water remained in the sump = L*B*H₁
⇒ 710000 = 150*100*H₁
⇒ H₁ = 710000/15000
⇒ H₁ = 47.33 cm
So, height of the water left in the sump is 47.33 cm
Answer.
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