A cylindrical water tank is 70cm in diameter.To begin with,it is full of water.A leak starts in the bottom so that it loses 10 liters of water every hour.How long will it take for the water level to fall by 20cm?

Answer 1

First, let's find the volume of water in the tank when it is full:

Radius of the tank = 70cm/2 = 35cm
Height of the tank = 70cm

Volume of a cylinder = πr^2h
Volume = π(35)^2(70)
Volume = 269150 cm^3

Given that the tank loses 10 liters (10000 cm^3) of water every hour, we can find out how long it will take for the water level to fall by 20cm:

Rate of water loss = 10000 cm^3/hour

Let x be the number of hours it takes for the water level to fall by 20cm.
Then, the volume of water lost in x hours = 10000x

After x hours, the height of the water in the tank will be reduced by 20cm, so the new height will be 50cm.

Volume of water left in the tank after x hours = π(35)^2(50)
Volume = 269150 - 10000x = π(35)^2(50)

Solving for x:

269150 - 10000x = 192500
-10000x = -76750
x = 7.675 hours

Therefore, it will take approximately 7.68 hours for the water level to fall by 20cm.