goal\nyour goal is to produce an estimate for the total cost of installing a pool for a customer of your…

goal\nyour goal is to produce an estimate for the total cost of installing a pool for a customer of your boss landscaping business.\nrole\nyou have been asked to compute the radius, diameter, and volume of the pool to be installed. then use that information to produce an estimate.\naudience\nyour target audience is your boss.\nsituation\nthe challenge involves dealing with a given equation to compute measurements for a pool then researching prices to produce an estimate.\nproduct, performance, and purpose\nyou will create an estimate in order to assist your boss in gaining the job! the equation that is given by the customer for the pool is (units are in feet): x2 + y2 = 81\nstandards and criteria for success\nyour performance needs to include the following calculations:\n - compute the radius and diameter of the pool.\n - compute the volume of water in the pool using the above calculations and a height of 4 ft.\n - assuming that water costs $0.22 per gallon and that pools cost $185 per foot of radius calculate the total cost of materials for the pool. keep in mind that there are 7.48 gallons of water per square foot.\n - assuming that a pool will take 2.5 hrs. per foot of radius, compute the total labor hours for the pool.\n - if you are to pay someone $19/hr, compute the total cost of labor.\n - find a total cost for the project.\n - all of the above is done showing all work.\n - a final paragraph that describes your steps and findings.\nplease upload your completed assignment here. be sure you have included your name at the top of your document and as part of the file name. be sure to review the rubric to see how you will be graded

goal\nyour goal is to produce an estimate for the total cost of installing a pool for a customer of your boss landscaping business.\nrole\nyou have been asked to compute the radius, diameter, and volume of the pool to be installed. then use that information to produce an estimate.\naudience\nyour target audience is your boss.\nsituation\nthe challenge involves dealing with a given equation to compute measurements for a pool then researching prices to produce an estimate.\nproduct, performance, and purpose\nyou will create an estimate in order to assist your boss in gaining the job! the equation that is given by the customer for the pool is (units are in feet): x2 + y2 = 81\nstandards and criteria for success\nyour performance needs to include the following calculations:\n - compute the radius and diameter of the pool.\n - compute the volume of water in the pool using the above calculations and a height of 4 ft.\n - assuming that water costs $0.22 per gallon and that pools cost $185 per foot of radius calculate the total cost of materials for the pool. keep in mind that there are 7.48 gallons of water per square foot.\n - assuming that a pool will take 2.5 hrs. per foot of radius, compute the total labor hours for the pool.\n - if you are to pay someone $19/hr, compute the total cost of labor.\n - find a total cost for the project.\n - all of the above is done showing all work.\n - a final paragraph that describes your steps and findings.\nplease upload your completed assignment here. be sure you have included your name at the top of your document and as part of the file name. be sure to review the rubric to see how you will be graded

Answer

Explanation:

Step1: Find the radius from the circle - equation

The standard form of a circle - equation is $(x - a)^2+(y - b)^2=r^2$. Given $x^{2}+y^{2}=81$, we have $r^{2}=81$, so $r = 9$ feet.

Step2: Calculate the diameter

The diameter $d$ of a circle is related to the radius by $d = 2r$. Substituting $r = 9$ feet, we get $d=2\times9 = 18$ feet.

Step3: Compute the volume of the pool

The pool is assumed to be a cylinder. The volume formula for a cylinder is $V=\pi r^{2}h$. Substituting $r = 9$ feet and $h = 4$ feet, we have $V=\pi\times9^{2}\times4=\pi\times81\times4 = 324\pi\approx324\times3.14 = 1017.36$ cubic - feet.

Step4: Calculate the cost of water

First, convert the volume from cubic - feet to gallons. Since there are 7.48 gallons per cubic - foot, the number of gallons of water $n=V\times7.48=1017.36\times7.48 = 7619.8528$ gallons. The cost of water $C_{w}=0.22\times n=0.22\times7619.8528\approx1676.37$ dollars.

Step5: Calculate the cost of the pool based on the radius

The cost of the pool based on the radius is $C_{p}=185\times r=185\times9 = 1665$ dollars.

Step6: Calculate the total material cost

The total material cost $C_{m}=C_{w}+C_{p}=1676.37 + 1665=3341.37$ dollars.

Step7: Calculate the total labor hours

The pool takes 2.5 hours per foot of radius. So the total labor hours $t = 2.5\times r=2.5\times9 = 22.5$ hours.

Step8: Calculate the total labor cost

The labor cost per hour is $19$ dollars. So the total labor cost $C_{l}=19\times t=19\times22.5 = 427.5$ dollars.

Step9: Calculate the total project cost

The total project cost $C = C_{m}+C_{l}=3341.37+427.5 = 3768.87$ dollars.

Answer:

The radius of the pool is 9 feet, the diameter is 18 feet, the volume of the pool is approximately 1017.36 cubic - feet, the total material cost is approximately 3341.37 dollars, the total labor cost is 427.5 dollars, and the total project cost is approximately 3768.87 dollars.