# calculus

posted by Sam

You are visiting your friend Fabio’s house. You ﬁnd that, as a joke, he ﬁlled his swimming pool with Kool-Aid, which dissolved perfectly into the water. However, now that you want to swim, you must remove all of the Kool-Aid contaminated water. The swimming pool is round, with a 15.5 foot radius. It is 8 feet tall and has 5 feet of water in it. How much work is required to remove all of the water by pumping it over the side? Use the physical deﬁnition of work, and the fact that the density of the Kool-Aid contaminated water is σ= 64.1lbs/ft3

1. Steve

1st way: figure the weight of a slice of water in the pool.

Integrate that weight through a height of its distance from the top.

2nd way: Figure the weight of all the water in the pool. Its center of mass is 5.5 feet from the top of the pool, so lift that weight 5.5 feet.

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