Answer:
40.72 gallons
Step-by-step explanation:
Since [tex]x = 18cos(\theta)[/tex] and [tex]y = 18sin(\theta)[/tex]. We can say this base has a shape of a circle of radius r = 18.
We can also calculate h in term of angle θ:
[tex]h(\theta) = 12 + \frac{36cos(\theta) - 18sin(\theta)}{6}[/tex]
[tex]h(\theta) = 12 + 6cos(\theta) - 3sin(\theta)[/tex]
We can calculate the area of the fence if we integrate this h function over θr, which is the chord length. θ ranges from 0 to 2π
A = ∫h(θ)rdθ
A = ∫(12 + 6cos(θ) - 3sin(θ))18d
A = (12θ + 6sin(θ) + 3cos(θ))18
As θ ranges from 0 to 2π as a full circle
A = (12*0 + 6sin(0) + 3cos(0))18 - (12*2π + 6sin(2π) + 3cos(2π))18
A = 3*18 - 18(24π + 3) = 1357.17 square yard
As 1 yard = 3 feet then 1 square yard = 9 square feet
1 gallon of paint can cover 300 square feet or 300 / 9 = 33.33 square yard
So to cover square yard Bob would need
1357.17 / 33.33 = 40.72 gallons of paint.
