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

True

False

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

True

False

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

True

False

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

True

False

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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