### Math Notes

Subjects

#### Differential Calculus Solutions

##### Topics || Problems

Water flows into a vertical cylindrical tank at 12 cu. ft. per min.; the surface rises at 6 in. per min. Find the radius of the tank.

Solution:

$$6 \frac{in}{min} = 0.5 \frac{ft}{min}$$

$$Vol = A_{base} h$$

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

$$12 = \pi r^2 (0.5)$$

$$r = \sqrt{\frac{12}{\pi(0.5)}} = 2.76 \text{ft}$$

The radius of the tank is approximately 2.76 ft.