A rectangular swimming pool 30 ft long, 15 ft wide, and 14...

A rectangular swimming pool 30 ft long, 15 ft wide, and 14 ft deep is filled with water to a depth of 12 ft. Use an integral to find the work required to pump all the water out over the top. (Take as the density of water ? = 62.4lb/ft3.) Work = 2751840 J Don't forget to enter units

Transcript

00:01 So here we have given with the dimensions of the rectangular swimming pool.

00:05 So i'm just drawing a schematic diagram over here first to solve this problem.

00:10 So let this be our rectangular swimming pool.

00:16 It was given that the swimming pool is having a depth of 15 feet.

00:22 So this is 14 feet.

00:25 So this is 14 feet depth swimming pool having a length of 50 feet the length is 50 feet i can join this line now here is the swimming pool we have now it was given that the water is up to a depth of 12 feet so this total depth over here is 14 so this is 14 feet so all the units are in feeds only so up to here this is 14 but water is up to this depth maybe so i can right in this blue color so water is up to this depth so i have this depth as 12 feet now the question was asked to find how much work should be done or how much work should be doing to take this water out of this swimming pool now for that what you would have to take first is let's take a small area over here let's take a small portion over here and this portion is having a depth of this small portion is having a depth of delta y so this depth is delta y and this area small area is delta a i can take sorry not area i'll be taking this volume over this part is delta v volume over this part is delta v so area of this small part will be equal to we know that this is having this like this rectangle is having rectangular is having rectangular is having a length of 50 feet so this length towards 50 feet and the width towards 10 feet so width is 10 feet so this area over here will be i mean the surface area over here will be 15 to 10 only that is 500 so area is will be always same because if i can draw that rectangular swimming pool over here this is the top view of the rectangular swimming pool.

02:48 This is how the rectangular swimming bowl is looks like from the top.

02:52 So this width will be 10 and this length will be 50...

Question

A rectangular swimming pool 30 ft long, 15 ft wide, and 14 ft deep is filled with water to a depth of 12 ft. Use an integral to find the work required to pump all the water out over the top. (Take as the density of water ? = 62.4lb/ft3.) Work = 2751840 J Don't forget to enter units

Please give Ace some feedback