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.