calculus
posted by soffy .
The crosssection of a drain is a trapezoid. The sides and the bottom of the trapezoid each have a length of 10 feet. Determine the angle θ such that the drain will have maximal crosssectional area.

For lack of specificity, I will let θ be the angle between the upper base and a side. I expect it will end up 90°, making a square crosssection, but let's wee what happens.
The height of the trapezoid will be 10sinθ, so the area is
a = 10sinθ (10+10+2*10cosθ)
= 10sinθ (20+20cosθ)
= 200sinθ (1+cosθ)
da/dθ = 200cosθ (1+cosθ) + 200sinθ(sinθ)
= 200(cos^2θ + cosθ  sin^2θ)
= 200(2cos^2θ+cosθ1)
da/dθ = 0 when cosθ = 1/2 or 1.
Looks like the max area occurs at θ=π/3
Looks like my gut feeling was wrong. Good thing, as it would have been a boring trapezoid. 
Oops. I forgot to divide by 2 when getting the average of the bases, but that does not affect the answer in this case.
Respond to this Question
Similar Questions

math
The cross section of an attic is in the shape of an isosceles trapezoid. If the height of the attic is 9 feet, BC=12 feet, and AD=28 feet, find the length of line AB to the nearest foot. The triangle of the trapezoid is triangle ABE … 
Geometry
An engineer designed a 620 ft long water canal to drain a rainwater detention pond. It is to have a trapezoid crosssection that is 8 ft deep, 15 ft across the bottom, with walls sloping outward at an angle of 40. (a)Calculate … 
calculus
a trapezoid is a quadrilateral with (only) two sides (called bases) that are parallel. an isosceles trapezoid has two equal legs. the area of a trapezoid is A=(1/2)*h*(b1+b2) where b1 and b2 are the two parallel bases and h is the … 
maths
A large canal will have a crosssection in the shape of an isosceles trapezoid. The top will be twice as wide as the bottom, and the depth will be 8.00 m. Because of the cost of the building materials, the bottom and two slopes sides … 
PHYSICS!!!
A liquid (ñ = 1.65 g/cm3) flows through a horizontal pipe of varying cross section as in the figure below. In the first section, the crosssectional area is 10.0 cm2, the flow speed is 288 cm/s, and the pressure is 1.20 105 Pa. In … 
Calculus
SOS...help!!! please email me at 969e221 at g mail. com here is the question: Find the trapezoid of largest area that can be inscribed in the upper half of the ellipse x2/9 + y2/4 = 1 where the lower base of the trapezoid is on the … 
Geometry
I have four questions: 1. The area of trapezoid ABCD is 60. One base is 4 units longer than the other, and the height of the trapezoid is 5. Find the length of the median of the trapezoid. 2. In trapezoid ABCD, line BC is parallel … 
math
The 2 parallel sides of a trapezoid measure 12 feet and 6 feet. If the height of the trapezoid is 7 feet. What is the area of the trapezoid? 
Calculus
The size of a parcel despatched through the post used to be limited by the fact that the sum of its length and girth (perimeter of the cross section) must not exceed 6 feet. What was the volume of the largest parcel of square cross … 
physics
a woman is draining her fish tank by siphoning the water into an outdoor drain the rectangular tank has footprint area A and depth H . the drain is located a distance D below the surface of the water in the tank , where D>>H …