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.

I want you to tell me HOW you would work this problem. You will find the answer, but you must show me all your steps.

Answer 1

Explanation:

To calculate the amount of sod and fence you need, follow these steps:

1. Find the circumference of the pool:

The distance across the pool through the center is the diameter, which is 15'. The circumference of a circle is found by multiplying the diameter by pi (approximately 3.14). So, the circumference of your pool is 15' x 3.14 = 47.1'.

2. Determine the length of fence needed: Since the fence will surround the pool in a square shape, each side of the square will be the same length. The middle of each side should be 8' from the edge of the pool. The distance from the center of the pool to the edge is the radius, which is half the diameter (15' / 2 = 7.5'). So,each side of the square will be 8' +

7.5' +7.5' = 23'.

To find the total length of fenceneeded, multiply the length of oneside by 4 (since there are four sidesin a square): 23' x 4 = 92'.

3. Calculate the area of the deck:The deck will be circular and have awidth of 4'. To find the radius of thedeck, subtract the pool's radius (7.5')from the radius of the deck plus thepool's radius (15' + 7.5' = 22.5'). So,the radius of the deck is 22.5' - 7.5'

= 15'.

The area of a circle is found bymultiplying the radius squared by pi.So, the area of the deck is 15' x 15' x3.14 = 706.5 square feet.

4. Determine the area of sod

needed:

The sod will be laid between the deck and the fence, forming a ring around the pool. To find the area of the sod, subtract the area of the pool (calculated using its radius of 7.5') from the area of the deck (calculated using its radius of 15').

The area of the pool is 7.5' x 7.5' x 3.14176.625 square feet.

So, the area of sod needed is 706.5 square feet - 176.625 square feet = 529.875 square feet.

Now you know that you need to purchase approximately 529.875 square feet of sod and 92 feet of fence.