A swimming pool is a rectangular solid 15 ft wide, 40 ft long, and at most 4 ft deep. Water is being added to the pool at the rate of 25 cubic ft per minute. How fast is the water rising when there is 1800 cubic ft of water in the pool?
calculus - Steve, Thursday, April 19, 2012 at 12:22pm
since the pool is a rectangular solid, it has a cross-section of constant size.
the pool is 15x40 = 600 ft^2
Thus, each ft of depth adds 600ft^3 of volume.
So, at 25ft^3/min, the height rises 25/600 = .0417 ft/min
Now, since this is for calculus class, they must want a solution involving related rates.
v = 40*15*x = 600x when the water is x feet deep.
dv/dt = 600 dx/dt
25 = 600 dx/dt
dx/dt = 25/600 = .0417