There exists a wall that is over 13,000 miles long. The length built during a particular dynasty is 5,500 miles. The cross section of the wall is a trapezoid 28 feet high, 22 feet wide at the bottom, and 16 feet wide at the top. How many cubic yards of material make up the (5,500 miles) portion of the wall?
I realize that I use the formula to solve area of the trapezoid but I do not know what comes next?
Thank You that help me understand the problem! And where does the 5280 come from? I do not understand that part?
the trapezoid is the base of the solid. As with all prisms, volume is base*height. (in this case, since the prism is lying on its side, it's the length of the wall)
v = (22+16)/2 * 28 * (1/5280)^2 * 5500 = 655/6336 mi^3
To find the volume of the portion of the wall, we first need to calculate the area of the trapezoid cross section.
The formula to find the area of a trapezoid is:
Area = (1/2) * (sum of the parallel sides) * (height)
In this case, the parallel sides are 22 feet and 16 feet, and the height is 28 feet.
Area = (1/2) * (22 + 16) * 28
= (1/2) * 38 * 28
= 532 square feet
Now we need to convert the length in miles to feet, considering that 1 mile equals 5,280 feet.
5,500 miles * 5,280 feet/mile = 29,040,000 feet.
Finally, we can calculate the volume of the portion of the wall by multiplying the area of the trapezoid by the length:
Volume = Area * Length
= 532 square feet * 29,040,000 feet
= 15,453,120,000 cubic feet
To convert cubic feet to cubic yards, we need to divide by 27 (since 1 cubic yard equals 27 cubic feet):
Volume = 15,453,120,000 cubic feet / 27
≈ 572,111,111.11 cubic yards
Therefore, the (5,500 miles) portion of the wall is composed of approximately 572,111,111.11 cubic yards of material.