How many cubic yards of concrete are required for a footing that is 75 feet long, given a cross-section with a 6 x 9 inch top face and a 6 x 12 inch bottom face?

How many cubic yards of concrete are required for a footing that is 75 feet long, given a cross-section with a 6 x 9 inch top face and a 6 x 12 inch bottom face?

• A. 2 cubic yards
• B. 2 1/2 cubic yards
• C. 2 3/4 cubic yards
• D. 3 cubic yards

Answer: (B)

You're being tested on volume of a footing with a trapezoidal cross-section. The length of the footing multiplies the cross-sectional area to give the total volume, and you must convert units consistently. The cross-section is a trapezoid with top width 9 inches, bottom width 12 inches, and a vertical thickness of 6 inches. Its area is (9 + 12) / 2 × 6 = 63 square inches. The footing runs 75 feet long, which is 75 × 12 = 900 inches. So the volume in cubic inches is 63 × 900 = 56,700 in^3. Convert to cubic yards: 1 cubic yard = 46,656 in^3, so 56,700 ÷ 46,656 ≈ 1.21 cubic yards. So about 1.21 cubic yards of concrete are needed.

You're being tested on volume of a footing with a trapezoidal cross-section. The length of the footing multiplies the cross-sectional area to give the total volume, and you must convert units consistently.

The cross-section is a trapezoid with top width 9 inches, bottom width 12 inches, and a vertical thickness of 6 inches. Its area is (9 + 12) / 2 × 6 = 63 square inches.

The footing runs 75 feet long, which is 75 × 12 = 900 inches. So the volume in cubic inches is 63 × 900 = 56,700 in^3.

Convert to cubic yards: 1 cubic yard = 46,656 in^3, so 56,700 ÷ 46,656 ≈ 1.21 cubic yards.

So about 1.21 cubic yards of concrete are needed.