### Math Notes

Subjects

#### Differential Calculus Solutions

##### Topics || Problems

Water is flowing into a vertical cylindrical tank at the rate of 24 cu. ft. per min. If the radius of the tank is 4ft. how fast is the surface rising?

Solution:

$$Vol =A_{base} h$$

The area of the base if constant, while the height is increase as water pours in.

$$\frac{dVol}{dt} = \frac{\pi 8^2}{4} \frac{dh}{dt}$$

$$24 = 16 \pi \frac{dh}{dt}$$

$$\frac{dh}{dt} = \frac{24}{16\pi} = 0.48 \frac{\text{ft}}{\text{min}}$$

The surface is rising at approximately 0.48 ft per min.