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Problem

Suppose that for the tank in Exercise 23 the pump…

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Problem 26 Hard Difficulty

A tank is full of water. Find the work required to pump the water out of the spout. In Exercises 25 and 26 use the fact that water weighs $ 62.5 lb/ft^3 $.


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Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 6

Applications of Integration

Section 4

Work

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Applications of Integration

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Watch More Solved Questions in Chapter 6

Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 22
Problem 23
Problem 24
Problem 25
Problem 26
Problem 27
Problem 28
Problem 29
Problem 30
Problem 31
Problem 32
Problem 33
Problem 34

Video Transcript

For this problem, we first need to get a geometry of the tank, so from a side view we're going to see a triangular with height to be 6 and the length to be 12. This is the side biloftank here and he thinks gonna get the equation that this segment for this line sat l and it's simply y equals to 6 over 12 x. So that means x equals to 2 y. That'S the equation of, and we divide volume by in horizontal slices and let y i stands for the height from the bottom of the earth. Slice of the water with sickness, delly and the tignis is it's a very thick slice and the volume equals to the area times the thickness so which is given by 10 times 2 y. I times and the force exerting on this infinitesimal volume is the volume self times the weight per unit volume so which is equals to 20 y. I times times 62.5, which is equal to 11250 y. I times delay that's the force and for each slice, the distance. That'S going to travel to get a job done is the i equal to 6 minus y. I is the total length till the height of tank is 66 feet on so here we're going to set up over roots its limits in and the i go goes from. 0 to n, f, delytis red or thinks it's flung it out here, just a 1250 times y i times and we're goin to evaluate this remansit by its corresponding integral so that 0 to 6, total height 1250 y times 6 minus y record that the distance it Could travel the way and after a long calculation i'm going to have 4.5 times 10 to the 4 feet? He.

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