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Chapter 6: Q. 27 (page 556)

The work required to pump all of the water out of a cone with top radius 3.5 feet and height 4 feet.

Short Answer

Expert verified

$W o r k d o n e = 15, 073, 100 J$

Step by step solution

01

Step1. Given Information

Top radius=3.5feet

height=4feet

02

Step2. Calculate

$1) . d V o l = A r e a d y = π r^{2} d y = π (5^{2} - y^{2}) d y 2) . d F = π (5^{2} - y^{2}) * 9800 3) . d w = d F * (4 - y) W = \int_{y 1}^{y 2} π (5^{2} - y^{2}) d y * 9800 * (4 - y) y 1 = - 5, y 2 = 0 = 9800 \int_{- 5}^{0} (5^{2} - y^{2}) (4 - y) d y = 9800 \int_{- 5}^{0} (100 - 25 y - 4 y^{2} + y^{3}) d y = 9800 {[100 y - \frac{25 y^{2}}{2} - \frac{4 y 3}{3} + \frac{y 4}{4}]}_{- 5}^{0} = 0 - 9800 [100 (- 5) - \frac{25 {(- 5)}^{2}}{2} - \frac{4 {(- 5)}^{3}}{3} + \frac{{(- 5)}^{4}}{4}] = 15, 073, 100 J$

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Most popular questions from this chapter

For each pair of definite integrals in exercise 13-18 decide which if either is larger without computing the integrals

$π \int_{0}^{2} x^{4} d x a n d π \int_{0}^{2} (x^{4} - 16) d x$

Use antidifferentiation and/or separation of variables to solve each of the initial-value problems in Exercises 29–52

$\frac{d y}{d x} = e^{x + y}, y (0) = 2$

find an equation that gives y as an implicit function of x. Then draw the continuous curve that satisfies this differential equation and passes through the point (2, 0).

$\frac{d y}{d x} = \frac{- x}{y}$

Find the exact value of the arc length of each function f(x) on [a, b] by writing the arc length as a definite integral and then solving that integral.

$f (x) = \sqrt{9 - x^{2}}$ , $[a, b] = [- 3, 3]$

Find the exact value of the arc length of each function f(x) on [a, b] by writing the arc length as a definite integral and then solving that integral.

$f (x) = \frac{1}{3} x^{3 / 2} - x^{1 / 2}$ , $[a, b] = [0, 1]$

See all solutions

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