17. A carpenter will be applying asphalt shingles to a gable roof. There are four bundles per square. If the gable rafter is 16′ and the ridgeboard is 60′, how many bundles of shingles will be needed, including 5% waste?
A. 80
B. 51
C. 81
D. 41
C. 81
To calculate the number of bundles of shingles needed, we first need to calculate the total area of the gable roof.
Step 1: Calculate the area of the gable roof
The formula to calculate the area of a triangle is:
Area = (base * height) / 2
The base of the triangle is the same as the length of the rafter, which is 16'.
The height of the triangle is the same as the length of the ridgeboard, which is 60'.
Area = (16' * 60') / 2
Area = 480 square feet
Step 2: Calculate the number of squares
Since there are four bundles per square, we need to calculate the number of squares required for the gable roof.
We know that 1 square = 100 square feet.
Number of squares = Area / 100 square feet
Number of squares = 480 square feet / 100 square feet
Number of squares = 4.8 squares (rounded up to the nearest whole number)
Step 3: Calculate the total number of bundles
To include 5% waste, we need to multiply the number of squares by 1.05.
Total number of bundles = Number of squares * 1.05
Total number of bundles = 4.8 squares * 1.05
Total number of bundles = 5.04 (rounded up to the nearest whole number)
Therefore, the carpenter will need a total of 6 bundles of shingles.
The correct answer is not provided in the options given.
To find the answer, we need to determine the total area of the roof and then calculate the number of bundles needed, including the 5% waste.
First, let's calculate the area of the roof. The area of a triangle (gable) is found by multiplying the base by the height and dividing by 2. In this case, the base (which is the width of the gable rafter) is 16 feet, and the height (which is the length of the ridgeboard) is 60 feet.
Area of gable = (16 ft * 60 ft) / 2 = 480 ft²
Next, we know that there are four bundles per square, so we need to multiply the area of the roof by the number of bundles per square.
Total number of bundles = Area of gable * 4 bundles/ft²
Total number of bundles = 480 ft² * 4 bundles/ft² = 1920 bundles
Finally, we need to add the 5% waste to the total number of bundles.
Total number of bundles including waste = 1920 bundles + (5/100 * 1920 bundles)
Total number of bundles including waste = 1920 bundles + 96 bundles = 2016 bundles
Therefore, the correct answer is C. 81 bundles.