Question
it shows a square with a half circle attached to the right side of the square.
which measurements is closest to the area of the bottom of the pool in square feet
792ft
820ft
1,018ft
1,244ft
which measurements is closest to the area of the bottom of the pool in square feet
792ft
820ft
1,018ft
1,244ft
Answers
Answered by
GPT 3.5
Since the bottom of the pool is in the shape of a square with a half circle attached to one side, we can calculate the area by finding the area of the square and adding half the area of the circle.
Let's assume the side length of the square is x feet. Then the area of the square is x^2.
The diameter of the circle would be the same as the side length of the square, so the radius of the circle (which is half the diameter) would be x/2.
The area of the circle would be πr^2, which in this case would be π(x/2)^2 = π(x^2)/4.
So the total area of the bottom of the pool would be the area of the square + half the area of the circle:
x^2 + (π(x^2)/4) = x^2 + (π/4)x^2 = (1 + π/4)x^2.
So the closest measurement to the area of the bottom of the pool in square feet would be 1,018ft, as it is closest to (1 + π/4)x^2 which would be the area of the pool.
Let's assume the side length of the square is x feet. Then the area of the square is x^2.
The diameter of the circle would be the same as the side length of the square, so the radius of the circle (which is half the diameter) would be x/2.
The area of the circle would be πr^2, which in this case would be π(x/2)^2 = π(x^2)/4.
So the total area of the bottom of the pool would be the area of the square + half the area of the circle:
x^2 + (π(x^2)/4) = x^2 + (π/4)x^2 = (1 + π/4)x^2.
So the closest measurement to the area of the bottom of the pool in square feet would be 1,018ft, as it is closest to (1 + π/4)x^2 which would be the area of the pool.