- #1

- 1,444

- 2

## Homework Statement

An industrial settling pond has a parabolic cross section described by the equation [itex] y = \frac{x^2}{80} [/itex]. the pond is 40 m across and 5 m deep at the cetner. the curved bottom surface of the pond is to be covered with a layer of clay to limit seepage from the pond. determine the surface are on the clay bottom of the pond

## Homework Equations

Length of a curve formula

[tex] ds = \sqrt{1+\left( \frac{dy}{dx} \right)^2 } [/tex]

## The Attempt at a Solution

I was thinking that if we simply find the length of the curve, then that would yield the surface area of the curve. This gives the following:

[tex] s = \int_{-20}^{20} \sqrt{1 + \frac{x^2}{1600} } dx [/tex]

Which gives an answer of 66.9

The answer however is 1332.2 m^2. This leads me suspect that we must include the fact that this curve is to be rotated around the y axis making a bowl. I am not sure how to rotate this curve though...

Your input is greatly appreciated!