Bet you can't solve: Calculus Work Problem

Question

A rectangular basement 30 feet long and 20 feet wide has been flooded with 3 ft of water. What is the amount of work required to pump the water out of the basement if the basement is 6 ft below ground level? The water weighs 62.3lbs per cubic foot. Any help is appreciated. Thanks.

Answer 1

Consider a cuboid of water, height dh, at distance h below the ground

Volume of the water is 30 x 20 x dh = 600 dh

Mass of this water = 62.3 x 500 dh = 31150 dh (lbs)

1 kg = 2.2 lbs, so this is 14159 dh kg

1 ft = 0.3 m approximately

We need to raise this water through h feet = 0.3 h metres

So work done = force x distance = mgh = 14159 x 9.81 x 0.3 h = 41670h J

So you just need to integrate this from h=3 to h=6

Giving [20835 h²] between limits 3 and 6, giving total work of 20835 x (36 - 9) = 562545 J