Differential Calculus Solutions
Topics || Problems
A rectangular trough is 10 ft long and 3 ft wide. Find how fast the surface rises, if water flows in at the rate of 12 cu. ft. per min.
Solution:
\(Vol = A_{base} h\)
\(\frac{dVol}{dt} = (3)(10)\frac{dh}{dt}\)
\(12 = 30 \frac{dh}{dt}\)
\(\frac{dh}{dt} = 0.4 fpm\)
The surfaces rises at 0.4 feet per minute.