Visualize a grassy yard that's measuring 40 feet by 20 feet. In the middle of the yard, imagine a round swimming pool with a diameter of 12 feet. To provide context, add a neighborhood backdrop as well. The pool is filled with sparkling, blue water on a sunny day. There's no text in this image.

A pool company will install a round swimming pool in the middle of a yard that measures 40 ft. by 20 ft. If the pool is 12 ft. in diameter, how much of the yard will still be available?:

466.86 ft2
762.32 ft2
686.96 ft2
347.84 ft2

yard 40*20 = 800

pool pi*(6^2) = 113.04
yard - pool
800 - 113.04
686.96

Well, once the round swimming pool is installed, the yard will definitely be feeling a bit "circled" out. But fear not, there will still be some space left for other activities!

To find out exactly how much space remains, let's first calculate the area of the whole yard. The formula to calculate the area of a rectangle is length times width, so in this case, that gives us 40 ft. times 20 ft., which equals 800 ft².

Next, we need to determine the area of the round swimming pool. The formula for the area of a circle is π times the radius squared. Since the pool has a diameter of 12 ft., the radius would be half of that, which is 6 ft. Applying the formula, we get π times 6 ft. squared, which is approximately 113.1 ft².

Finally, to find out how much of the yard is still available, we subtract the area of the pool from the total area of the yard. So, 800 ft² minus 113.1 ft² equals approximately 686.9 ft².

Therefore, the correct answer is 686.96 ft² of the yard will still be available for other things, like sunbathing, playing frisbee, or perhaps starting a tiny lemonade stand.

To find out how much of the yard will still be available, we first need to calculate the area of the pool and then subtract it from the total area of the yard.

1. Area of the pool:
The pool is round, so we can use the formula for the area of a circle: A = πr², where A is the area and r is the radius. The diameter of the pool is 12 ft, so the radius (r) is half of that, which is 6 ft.

A = π(6 ft)²
A = π(36 ft²)
A ≈ 113.1 ft²

2. Area of the yard:
The yard measures 40 ft by 20 ft, so the total area is the product of these two dimensions.

A = (40 ft)(20 ft)
A = 800 ft²

3. Calculation of available space:
To find out how much of the yard will still be available, we need to subtract the area of the pool from the total area of the yard.

Available space = Total area of yard - Area of pool
Available space = 800 ft² - 113.1 ft²
Available space ≈ 686.9 ft²

Therefore, the correct answer is 686.96 ft².

To find out how much of the yard will still be available, we need to calculate the area of the yard and subtract the area of the pool.

First, calculate the area of the yard by multiplying the length and width:
Area of yard = Length * Width = 40 ft * 20 ft = 800 ft^2.

Next, calculate the area of the pool using the formula for the area of a circle:
Area of pool = π * (radius)^2, where radius = diameter / 2 = 12 ft / 2 = 6 ft.
Area of pool = 3.14 * (6 ft)^2 = 113.04 ft^2 (approx).

Finally, subtract the area of the pool from the area of the yard to find the remaining available space:
Remaining area = Area of yard - Area of pool = 800 ft^2 - 113.04 ft^2 = 686.96 ft^2.

Therefore, the answer is: 686.96 ft^2.