Find the cost of sod, at $0.49 per square foot, for a playing field that has a semi circle on each end with the radius of 8ft. Show work.
Answer: $325.83
What kind of playing field?
you don't give the length of the playing field, but it must have a width of 16 ft.
So, given a length of x, we must have
(16x+64π)*0.49 = 325.83
So, I guess the length must be 29 ft.
To find the cost of sod for the playing field, we need to calculate the area of the entire field, including the semi-circles on each end. Then, we will multiply this area by the cost per square foot.
Let's break down the process step-by-step:
1. Calculate the area of the rectangular portion of the playing field:
The length of the rectangular portion is the total length minus the diameter of the semi-circle on each end.
Given that the radius of each semi-circle is 8ft, the diameter is 2 times the radius, which is 2 * 8ft = 16ft.
So, the length of the rectangular portion is the total length minus 16ft.
Let's assume the total length is L ft.
Then, the length of the rectangular portion is (L - 16) ft.
The width of the rectangular portion will be the width of the entire field.
Therefore, the area of the rectangular portion is (L - 16) * W ft².
2. Calculate the area of a semi-circle:
The area of a semi-circle is half the area of a full circle.
The formula to calculate the area of a full circle is A = πr², where A is the area and r is the radius.
Given that the radius of each semi-circle is 8ft, the area of each semi-circle will be (1/2) * π * (8 ft)².
3. Calculate the total area of the playing field:
The total area of the playing field is the sum of the area of the rectangular portion and the area of the two semi-circles.
So, the total area is (L - 16) * W ft² + 2 * [(1/2) * π * (8 ft)²].
4. Calculate the cost of the sod:
Multiply the total area (in square feet) by the cost per square foot, which is $0.49.
Therefore, the cost of sod = Total area * Cost per square foot.
Putting it all together:
Cost of sod = [(L - 16) * W + 2 * (1/2) * π * (8 ft)² ] * $0.49
To find the exact cost, we will need the width (W) and the total length (L) of the playing field. Once we have those values, we can plug them in this formula and calculate the answer.