Question

A tank of water has base a circle of radius 2 meters and vertical sides. If water leaves the tank at a rate of 5 liters per minute, how fast is the water level falling in centimeters per hour? (Remember that 1 liter is 1000 cubic centimeters.)

Answer 1

Answer:

0.0398cm/min

Step-by-step explanation:

We are given that

Radius of base circle=r=2 m=$2\times 100=200 cm$

1 m=100 cm

$\frac{dV}{dt}=5L/minute=5000cm^3/min$

1 L=1000 cubic cm

We know that

Volume of tank=$\pi r^2 h$

Differentiate w.r.t t

$\frac{dV}{dt}=\pi r^2\frac{dh}{dt}$

Substitute the values

$5000=\pi(200)^2\frac{dh}{dt}$

$\frac{dh}{dt}=\frac{5000}{\pi(200)^2}=0.0398cm/min$