Problem 21 Medium Difficulty

Show how to approximate the required work by a Riemann sum. Then express the work as an integral and evaluate it.

An aquarium 2 m long, 1 m wide, and 1 m deep is full of water. Find the work needed to pump half of the water out of the aquarium. (Use the fact that the density of water is $ 1000 kg/m^3 $.)

Answer

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Video Transcript

technically, the works that's gonna lived our waters from the the quarry in That's first government with the geometry, this problem, we're gonna send them a co ordinates along a quote a quarry in. So this is like a zero on this away with one cause the death of the cornice one I think of a slice a thing slice of water that's gonna be over elements of our women. Some. If you want to leave this thing, slice by ex meter. See why murder? Because this is our ordinance the force is gonna do that is ethical, Sevgi. He goes to to roll down the white SG. We know that row is worth 1000 ji is 9.8. So we're gonna plug. You know this better later. So the force is gonna be done by letting one slice is going F Times X. Why here? Because where think of Oracle, Vertical says happens. Why equals two to Rome that away g Why? And the work is represented by integrating this immigrants, right? So to throw that away, G y. And here this is a This is the expression in the women's cell and for integral to replace the wake, the other. Why? Because it's approaching zero. I like the way he so the total value that it's too. 2450 Joel.