Posted by Mindy on Sunday, October 16, 2011 at 10:55pm.
my circular swimming pool has a 29 foot diameter and is 8 feet tall. at the beginning of the summer i need to fill the pool with water. the flow rate from my spigot into the pool is about 0.75 cubic feet per minute. how fast is the water level, h, rising at the moment when the water level is at a height is 3.7 feet. Plus find the equation relating the two changing quantities.

calculus  Steve, Monday, October 17, 2011 at 1:29pm
The pool has Volume = π * 29^2 * 8/4 = 1682π ft^3
However, the water h feet deep has volume π * 29^2 * 1/4 * h ft^3 = 210.25πh ft^3
V = 841πh/4
dV = 841π/4 dh
0.75 = 841π/4 dh
dh = 0.00113544 ft/min
This rate does not change, since the pool has a circular crosssection, and the radius is constant.
Not only that, it will take 8/0.00028386 = 7045 min to fill the pool. That's 4.9 days!
Answer This Question
Related Questions
 Calculus  Suppose that water is pouring into a swimming pool in the shape of a ...
 calculus  Suppose that water is pouring into a swimming pool in the shape of a ...
 math  calculus  Suppose that water is pouring into a swimming pool in the ...
 Math  A circular swimming pool is 4 feet deep and has a diameter of 15 feet. If...
 Math  A circular swimming pool is 4 feet deep and has a diameter of 15 feet. If...
 Math  Suppose that water is pouring into a swimming pool in the shape of a ...
 Algebra 1  A circular pool has a diameter of 12 feet. The pool is 5 feet deep ...
 math  A circular pool has a diameter of 12 feet. The pool is 5 feet deep ...
 algebra 2  an empty swimming pool is shaped like a rectangular prism with a ...
 Math  A swimming pool size is 42 m long and 55 m wide with an average depth of ...
More Related Questions