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A house contains an above ground swimming pool in the shape of a circular cylinder. The radius of the cylindrical pool is 12 feet, and the height is 4 feet. At time $t = 0$ hours, the pool contains 1,000 cubic feet of water. During the next 12 hours ($t = 0$ until $t = 12$), water is pumped into the pool at a rate of $P(t)$ cubic feet per hour. During the same time interval, water is leaking from hole in the side of the pool at a rate of $L(t)$ cubic feet per hour. The table below gives values of the pumping rate and leaking rate every two hours between $t = 0$ and $t = 12$.

In the sortable table below, click on the column title to organize the table by that column's values.

Time Pumping Rate P(t) Leak Rate L(t)
0 10 13
1 13 15
2 16 16
3 20 19
4 24 20
5 25 19
6 23 16
7 20 14
8 15 12
9 13 10
10 12 12
11 11 13
12 10 14

Decide whether the following statements are true or false.

True

False

The water level of the pool is rising at the greatest rate at t = 5.

The water level of the pool reaches its greatest height at t = 5.

The pool will have a greater volume of water at t = 12 than at t = 0.

By t = 12, the height of the water is more than 60% of the way to the top of the pool.

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