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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Chapter 6

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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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Problem

Suppose that for the tank in Exercise 23 the pump…

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Calculus: Early Transcendentals

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Watch More Solved Questions in Chapter 6

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James Stewart

Calculus: Early Transcendentals

Grace He

Heather Zimmers

Samuel Hannah

Michael Jacobsen

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Calculus: Early Transcendentals

Grace He

Heather Zimmers

Samuel Hannah

Michael Jacobsen

James StewartCalculus: Early Transcendentals

Grace He

Heather Zimmers

Samuel Hannah

Michael Jacobsen

James Stewart

Calculus: Early Transcendentals