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Show how to approximate the required work by a Riemann sum. Then express the work as an integral and evaluate it.
A spherical water tank, 24 ft in diameter, sits atop a 60 ft tower. The tank is filled by a hose attached to the bottom of the sphere. If a 1.5 horsepower pump is used to deliver water up to the tank, how long will it take to fill the tank? (One horsepower = 550 ft-lb of work per second.)
$16 h, 30 \mathrm{~min}$
Calculus 2 / BC
Chapter 6
Applications of Integration
Section 4
Work
Harvey Mudd College
University of Michigan - Ann Arbor
University of Nottingham
Idaho State University
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for this question were asked to calculate the time they're required to 2,000,000,000 ting eso here. We're gonna use this one there. That walk the work equals to the power comes the time we're looking for the time. So time English too worked up over power and how to calculate the words we're gonna use the energy to technical work. So the work that we're gonna feel really the tank equals to the potential energy of all the water and the petition energy of water is actually the the weight of the water times the highly water So the weight of the water see em. Water equals to the desert water times the ballroom, a clover, tink and kiss Our tank is a, um this American Tink. So we do supply. Oh, we're to supply the form there for a spare the bottom of a spare. So that is thrilled for pi times the radius tell Cube in terms visit water, which is given by 62 15 So, um, that's over mass. So the way of the water and the energy equals to the work equals two. The weight of the water times to hide the water and that equals two, um, this December. Let's just calculated Cool later, Okay? And h here, we know that, uh, we just use LBO letters, and we're plugging ever. Well, you understand the height here is 72 feet. Okay, So the last step is to divide it to divide this work by the power and C equals two zombie over P. So that's and James H. Over P. And he here we know is 550. What's and this is roughly we'll talk another battle and calculated It's roughly Oh, 16 hours, 30 minutes.
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