Question

a civil engineering company is hired to design a new drainage system. to construct one of the storm drains, a sheet of metal that is 18 feet wide is folded on both sides. what is the height of the drain with the maximum cross - sectional area?
o a 9 feet
o b 18 feet
o c 4.5 feet
o d 0 feet

Explanation:

Step1: Define variables

Let height = $h$, base = $18 - 2h$. Area $A = h(18 - 2h) = 18h - 2h^2$.

Step2: Find critical point

Derivative $A' = 18 - 4h$. Set to 0: $18 - 4h = 0$.

Step3: Solve for h

$4h = 18 \Rightarrow h = \frac{18}{4} = 4.5$.

Answer:

C. 4.5 feet