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?: *
Subtract the pool area from the yard area
Well, let me put on my swimming goggles and calculate that for you! So, the area of the yard is 40 ft. by 20 ft., which equals 800 sq. ft. The area of the round pool with a diameter of 12 ft. is approximately 113.1 sq. ft. Now, if we subtract the pool area from the yard area, we get 800 sq. ft. - 113.1 sq. ft., which leaves us with approximately 686.9 sq. ft. of yard still available. That's enough space for a game of pool noodle limbo!
To find out how much of the yard will still be available after installing the round swimming pool, we need to calculate the area of the pool and subtract it from the total area of the yard.
1. Calculate the area of the pool:
The pool is round, so we can use the formula for the area of a circle: A = πr^2
Given that the diameter of the pool is 12 ft, the radius (r) is half of that, which is 12/2 = 6 ft.
Plugging the radius into the formula, we get: A = π(6)^2 ≈ 113.1 sq ft.
2. Calculate the area of the yard:
The yard measures 40 ft by 20 ft, so its total area is calculated by multiplying the length by the width: A = 40 ft × 20 ft = 800 sq ft.
3. Calculate the remaining area of the yard:
To determine how much of the yard will still be available, we subtract the area of the pool from the total area of the yard:
Remaining area = Total area of yard - Area of pool
Remaining area = 800 sq ft - 113.1 sq ft ≈ 686.9 sq ft.
Therefore, approximately 686.9 square feet of the yard will still be available.
To determine how much of the yard will still be available after the pool installation, we need to calculate the area of the yard and subtract the area of the pool.
The yard measures 40 ft. by 20 ft., which means it has a total area of 40 ft. x 20 ft. = 800 sq. ft.
The pool has a diameter of 12 ft., so the radius will be half of that, which is 12 ft. / 2 = 6 ft. The area of a circle is given by the formula A = πr², where A is the area and r is the radius.
The area of the pool is therefore A = π x (6 ft.)² = 36π sq. ft.
To find out how much of the yard will still be available, we subtract the area of the pool from the total yard area:
Available yard area = Total yard area - Pool area
= 800 sq. ft. - 36π sq. ft.
So, the amount of yard still available will be approximately 800 sq. ft. - 36π sq. ft.
Please note that the value of π (pi) is approximately 3.14159, so to get a more precise answer, you would need to use the actual value of π.