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? : *
A) 466.86 ft2
B) 762.32 ft2
C) 686.96 ft2
D) 347.84 ft2
First, we need to calculate the area of the yard:
Area of the yard = Length x Width
Area of the yard = 40 ft x 20 ft
Area of the yard = 800 ft2
Next, we need to calculate the area of the pool:
Area of the pool = πr^2
Area of the pool = π(6 ft)^2
Area of the pool = π(36 ft2)
Area of the pool = 113.097 ft2
Now, we subtract the area of the pool from the area of the yard to find out how much of the yard will still be available:
Available yard area = Area of the yard - Area of the pool
Available yard area = 800 ft2 - 113.097 ft2
Available yard area = 686.903 ft^2
Therefore, the answer is rounded to 686.96 ft2, so the correct option is C) 686.96 ft2.