PART A
The barn is constructed by the following 2D shapes
Two triangles of height = 4' and base = 20'
Area = 2 × (0.5×4×20) = 80
Two rectangles of length = 20' and width = 15'
Area = 2 × 20 × 15 = 600
Two rectangles of length = 45' and width = 15'
Area = 2 × 45' × 15' = 1350
One base of length = 45' and width = 15'
Area = 45 × 15 = 675
Two rectangles on each on one side of the roof. We have the length = 45' but not the width. We can work out the width by using Pythagoras theorem
w² = 4² + 10²
w² = 16 + 100
w² = 116
w = √116 = 10.77
Area of the two rectangles on the roof part is = 2 ×10.77 × 45 = 969.33
Total area to paint = 969.33+675+1350+600+80 = 3674.33 ≈ 3700 (to the nearest hundreth)
PART B
Numbers of paint cans needed = 3700 ÷ 57 = 64.9 ≈ 65 cans
PART C
Total cost of paint = 65 × 23.50 = $1527.50
PART D
The barn is constructed by a cuboid and a rectangular prism
V of cuboid = length × width × height
V of cuboid = 20 × 45 × 15
V of cuboid = 13500
V of triangular prism = Area of cross section × depth
V = [0.5×4×20] × 45
V = 1800
Total volume = 1800 + 13500 = 15300
is the sum of nth term (we want to figure this out for first 36 terms)
is the first term (we figured this out to be 9.625)
is the term number (36 for our case)
is the common difference (given as
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