The city has decided to build a circular outdoor amphitheater in the new park. The architects would like to surround the amphitheater with a 1 foot high brick wall and lay turf inside. They would like the diameter of the amphitheater to be 140 feet. The city has provided a budget of $60,000 for this project.

a. The brick wall is estimated to cost $80.00 per foot. What is the cost for the brick wall? Use 3.14 for π.

b. The turf is estimated to cost $3.00 per square foot. What will be the cost for the turf? Use 3.14 for π.

c. Can the city complete this project and stay within the budget? Explain.

Question

Mathematics

Ruth Hawkins

24 August, 23:13

The city has decided to build a circular outdoor amphitheater in the new park. The architects would like to surround the amphitheater with a 1 foot high brick wall and lay turf inside. They would like the diameter of the amphitheater to be 140 feet. The city has provided a budget of $60,000 for this project.

a. The brick wall is estimated to cost $80.00 per foot. What is the cost for the brick wall? Use 3.14 for π.

b. The turf is estimated to cost $3.00 per square foot. What will be the cost for the turf? Use 3.14 for π.

c. Can the city complete this project and stay within the budget? Explain.

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Answers (1)

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Ezekiel Case · Answer 1

Answer: (A) The cost for the brick wall is $35,168

(B) The cost for the turf is $46,158

(C) The city cannot stay within the budget

Step-by-step explanation: The brick wall meant to surround the amphitheater is equivalent to the circumference of the amphitheater itself, so we shall start by calculating the circumference of the amphitheater. We know the radius is 70 feet since the diameter has been given as 140 feet. The circumference of a circular shape is given as,

Circumference = 2Pi x r

Circumference = 2 x 3.14 x 70

Circumference = 70 x 3.14

Circumference = 439.6

Having been told that the brick wall costs $80 per foot, and the total brick wall is 439.6 feet, the cost of the entire brick wall shall be calculated as;

Cost = 439.6 x 80

Cost = 35168

The cost of the brick wall therefore is $35,168.

The turf to be laid inside is equivalent to the area of the amphitheater, hence we shall now calculate the area. The area of a circular shape is given as;

Area = Pi x r^2

Area = 3.14 x 70^2

Area = 3.14 x 4900

Area = 15386

If the turf would cost $3 per square foot, and the entire turf is 15386, then the total cost would be calculated as,

Cost = 15386 x 3

Cost = 46158

Therefore the total cost of the turf would be $46,158.

Remembering that the city has already budgeted $60,000 for the project, if we add the cost of brick wall and turf together we shall have a total cost of $81,326. This is already beyond the amount budgeted and so the city cannot complete the project.