# Math Help - trapezoidal section

1. ## trapezoidal section

Evening all.

Im getting stuck on a question that I just cant figure out.

I'll relay it below and if anyone could offer some help it would be much appreciated.

A cooling tank is to be made with a trapezoidal section as shown below. Calculate for a minimum width W, the material needed to form the bottom and folded sides.

45° \_CSA=300000mm2_/ 45°
¦<---- W --------->¦

Hope the crude drawing works but all I have is a CSA and the angles of the sides. Many thanks

2. Originally Posted by haverford
Evening all.

Im getting stuck on a question that I just cant figure out.

I'll relay it below and if anyone could offer some help it would be much appreciated.

A cooling tank is to be made with a trapezoidal section as shown below. Calculate for a minimum width W, the material needed to form the bottom and folded sides.

45° \_CSA=300000mm2_/ 45°
¦<---- W --------->¦

Hope the crude drawing works but all I have is a CSA and the angles of the sides. Many thanks
I'm not certain that I understand your question correctly but I'll give it a try:

1. I assume that you are asked to minimize the material used to form the bottom and the 2 slanted sides of the tank. If so:

Let L denote the complete length (2 slanted sides and the bottom):

$L = w + 2s$

2. The cross section of the tank consist of a rectangle and a square which is formed by the two right isosceles triangles:

$s = h \cdot \sqrt{2}$

$a = w \cdot h + h^2$

With a = 300,000 mm² you get: $w = \frac{300,000-h^2}h$

3. Plug in these terms into the equation of L:

$L(h)= \frac{300,000-h^2}h + 2 h \sqrt{2}$

4. Differentiate L wrt h and solve the equation L'(h) = 0 for h.

5. Plug in the calculated value of h into the equation of w.

6. For confirmation only: I've got w = 335.56 mm

3. thank you very much for your help