23% Thu 12-19 Bookmarks Window Help webwork3 math utahedu Logged in as c-wrt wor

Question

23% Thu 12-19 Bookmarks Window Help webwork3 math utahedu Logged in as c-wrt work Log out MATHEMATICAL ASSOCIATION OF AMERICA math 210fall2016-90 10 webwork 11: Problem 10 Prev Up Next 1 pt) Find the work done in pumping the water over the rim of a tank that is 50feet long and has a semicircular end of radius 10 feet if the tank is filled to a depth of 6 feet. foot-pounds Please check Page 304. Example 3,Figure 7. Preview Answers Submit Answers You have attempted this problem 0 times. Your overall recorded score is 0% You have unlimited attempts remaining ed at 12/08/2016 at 12:19pm MST WeBWorK C 1996-20 The WeBWorK Project MacBook Air

Explanation / Answer

You didn't say how the tank was oriented. Is the widest width (20 ft) at the top? I am going to assume that it is. The problem in the case that the greatest width is on the bottom is similar, but the setup is different.

Let x represent the distance from the top of the tank (it's widest point) to a point lower towards the bottom of the tank in a vertical direction. Consider a rectangular section of the tank that is x feet from the top and dx high. The weight of this section is 2 * (10^2 - x^2)^(1/2) * 50 * dx * D * g, where D represents the density of water. You must choose appropriate units. Converting the dimensions to meters would be my choice since the density of water is an easy 1000 kilograms per cubic meter. This section must be lifted the distance x to get it to the top of the tank, so the work done moving it is x * 2 * (10^2 - x^2)^(1/2) * 50 * dx * D * g. Now, you integrate this from x = 4 to x = 10 to find the total work done to empty the tank.

Related Questions

Navigate

• Browse (All)
• Browse 2
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.