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A concrete retaining wall is 120 feet long with ends shaped as given. How many cubic yards of concrete are required to construct the wall?
a. 217.8 yd3
b. 5,880 yd3
c. 653.3 yd3
d. 49 yd3
a. To determine how many cubic yards of concrete are required to construct the wall, we must evaluate the volume of the wall. The volume of the wall is determine by ?nding the surface area of the end and multiplying it by the length of the wall, 120 ft. The surface area of the wall is found by dividing it into three regions, evaluting each region's area, and adding them together. The regions are labeled A, B, and C. To determine the area of region A, multiply the length (3) times the height (10) for an area of 30 ft2. To evaluate the area of region B, multiply the length (5) times the height (3) for an area of 15 ft2. To evaluate the area of region C, multiply 1 timesthe base (2) times the height (4) for an area of 4 ft2. The surface area of the end is 30 ft2 + 15 ft2 + 4 ft2 or 49 ft2. Multiply 49 ft2 by the length of the wall 120 ft; 5,880 ft3 is the volume of the wall. The question, however, asks for the answer in cubic yards. To convert cubic feet to cubic yards, divide 5,880 ft3 by 27 ft3, the number of cubic feet in one cubic yard, which equals 217.8 yd3. If you select b, you did not convert to yd3. If you select c, the conversion to cubic yards was incorrect. You divided 5,880 by 9 rather than 27. If you select d, you found the area of the end of the wall and not the volume of the wall.
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