
Concept explainers
(a)
To find: The area of trapezoidal cross section of the dam.
(a)

Answer to Problem 30PPS
The area of trapezoidal cross section of the dam is 1110h2−30h .
Explanation of Solution
Given information:
Given a new dam being built has the shape of a trapezoid. The base at the bottom of the dam is 2 times the height. The base at the top of the dam is times the height minus 30 feet.
Calculation:
Calculate the expression
Then the equation for the area of a trapezoid:
A=12(b1+b2)hwhere,b1=2hb2=15h−30
Then Area:
A=12(b1+b2)h=12(2h+(15h−30))h=12(115h−30)h=1110h2−30h
Therefore, the area of trapezoidal cross section of the dam is 1110h2−30h .
(b)
To find: The area of this cross section, if the height of the dam is 180 feet.
(b)

Answer to Problem 30PPS
The area is 32940 square feet
Explanation of Solution
Given information:
Given a new dam being built has the shape of a trapezoid. The base at the bottom of the dam is 2 times the height. The base at the top of the dam is times the height minus 30 feet.
Calculation:
Calculate the expression
If the height of the dam is h=180 feet, then the area of this cross section:
1110h2−30h=1110(180)2−30(180)=1110(32400)−2700=35640−2700=32940
Therefore, the area is 32940 square feet.
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