A building has an area of 3,350 square feet and a roof slope of 3 in 12. If shingles are sold in bundles of three per square, how many bundles are required (no waste allowance)?

A building has an area of 3,350 square feet and a roof slope of 3 in 12. If shingles are sold in bundles of three per square, how many bundles are required (no waste allowance)?

• A. 103
• B. 104
• C. 105
• D. 106

Answer: (B)

Understanding how slope changes the roof area and how shingles are sold is the key. A roof with a 3 in 12 slope rises 3 units for every 12 units of horizontal run, so the actual roof surface is a bit larger than the plan area. The slope factor is sqrt(1 + (rise/run)^2) = sqrt(1 + (3/12)^2) = sqrt(1 + 0.25^2) = sqrt(1.0625) ≈ 1.0308. Multiply the horizontal area by this factor: 3,350 × 1.0308 ≈ 3,453 square feet of roof. Shingles are sold by the square, with 1 square covering 100 square feet, and each square comes in 3 bundles. So the number of bundles needed is the roof area times 0.03 (bundles per square foot): 3,453 × 0.03 ≈ 103.59 bundles. Since you can’t buy a fraction of a bundle and there’s no waste allowance, round up to the next whole bundle: 104 bundles.

Understanding how slope changes the roof area and how shingles are sold is the key. A roof with a 3 in 12 slope rises 3 units for every 12 units of horizontal run, so the actual roof surface is a bit larger than the plan area. The slope factor is sqrt(1 + (rise/run)^2) = sqrt(1 + (3/12)^2) = sqrt(1 + 0.25^2) = sqrt(1.0625) ≈ 1.0308. Multiply the horizontal area by this factor: 3,350 × 1.0308 ≈ 3,453 square feet of roof.

Shingles are sold by the square, with 1 square covering 100 square feet, and each square comes in 3 bundles. So the number of bundles needed is the roof area times 0.03 (bundles per square foot): 3,453 × 0.03 ≈ 103.59 bundles. Since you can’t buy a fraction of a bundle and there’s no waste allowance, round up to the next whole bundle: 104 bundles.