Question

My swimming pool is round. It measures 15' across from one side to the other through the center of the pool. It is 5’ deep. I am putting up a fence. I want the fence to be a square. The middle of each side of the fence needs to be 8' from the edge of the circle. (The circle is in the middle of the fence.) I then want to build a deck around the pool. It will be 4' across and will circle the pool. The deck will be a circle, not a square. Last thing I want to do is to lay sod (grass) between the deck and the fence.

I need to know how much sod to purchase and how much fence to purchase.

Please show work step by step

Answer 1

To determine the amount of sod to purchase and the length of the fence, we need to calculate the areas of the deck and the grassy area between the deck and the fence, as well as the circumference of the fence circle. The area of the deck is 415.57 square feet, the area of the grassy area is 339.09 square feet, and the length of one side of the fence is 24.36 feet.

Step-by-step explanation:

To find out how much sod to purchase, we need to calculate the area of the grassy area between the deck and the fence. The deck is 4' wide and circles the pool, so its diameter is 15' + 4' + 4' = 23'. The radius of the deck is half the diameter, so it is 23'/2 = 11.5'. The area of the deck is calculated using the formula for the area of a circle, which is A = πr^2, where r is the radius. Therefore, the area of the deck is A = 3.14 * (11.5')^2 = 415.57 square feet.

To calculate the area of the grassy area between the deck and the fence, we need to subtract the area of the deck from the area of the larger circle formed by the fence. The diameter of the fence circle is 15' + 8' + 8' = 31', so the radius is 31'/2 = 15.5'. The area of the fence circle is A = 3.14 * (15.5')^2 = 754.66 square feet. Therefore, the area of the grassy area is 754.66 square feet - 415.57 square feet = 339.09 square feet.

To determine how much sod to purchase, you should measure the area of the grassy area between the deck and the fence, which is 339.09 square feet.

To calculate the length of the fence, we need to find the circumference of the larger circle formed by the fence. The circumference of a circle is calculated using the formula C = 2πr, where r is the radius. Therefore, the circumference of the fence circle is C = 2 * 3.14 * 15.5' = 97.44 feet. Remember, the fence is square, so we need to divide the circumference by 4 to get the length of one side of the fence. Therefore, the length of one side of the fence is 97.44 feet / 4 = 24.36 feet.

To determine how much fence to purchase, you should measure the length of one side of the fence, which is 24.36 feet.

Answer 2

Answer:Fence = 124 feet

sod ≈ 545.3572

Step-by-step explanation:

1) For fence we need to calculate length of side of square

The pool is round with a diameter of 15', so the radius is 15'/2 = 7.5'.

The middle of each side of the square fence needs to be 8' from the edge of the circle. This means the side of the square fence is 2×(7.5+8)=31′ (adding the radius of the pool and the distance from the center to the fence).

The perimeter of a square is 4×side length, so the total length of fence needed is

4×31′=124 feet

2)For Sod we need to calculate area of swimming pool including Deck and subtract it from outer fence area

Area of swimming pool including Deck

total Diameter = 15+4+4=23

so Radius=23/2

area of swimming pool including Deck=(23x23x22)/(2x2x7)≈415.6428

Outer fence area

side x side=31 x 31= 961

therefore total sod needed is 961-415.6428=545.3572 sq ft