A solid concrete dam is to be built to hold back a depth \(D\) of water. For ease of construction the walls of the dam must be planar. Your supervisor asks you to consider the following dam cross-sections: a rectangle, a right triangle with the hypotenuse in contact with the water, and a right triangle with the vertical in contact with the water. The supervisor wishes you to determine which of these would require the least amount of concrete. What will your report say? You decide to look at one more possibility: a nonright triangle, as shown. Develop and plot an expression for the cross-section area \(A\) as a function of \(a\), and find the minimum cross-sectional area.

Transcribed Image Text:

D Water ab b P3.56