A circle is cut from a square piece of cloth, as shown:
A square, one side labeled as 36 inches, has a circle inside it. The circle touches all the sides of the square. The portion of the square outside the circle is shaded.
How many square inches of cloth are cut from the square? (5 points)
(π = 3.14)
1,017.36 in2
1,489.24 in2
1,182.96 in2
1,276.00 in2
To find the area of the shaded portion outside the circle, we first need to find the area of the circle and then subtract it from the area of the square.
The area of the circle can be calculated using the formula A = πr^2, where r is the radius of the circle. Since the circle touches all sides of the square, the diagonal of the square is equal to the diameter of the circle. The diagonal of the square can be calculated using the Pythagorean theorem:
Diagonal^2 = Side^2 + Side^2
Diagonal^2 = 36^2 + 36^2
Diagonal^2 = 1296 + 1296
Diagonal^2 = 2592
Diagonal = √2592
Diagonal ≈ 50.91 inches
Diameter = 50.91 inches
Radius = Diameter / 2
Radius = 50.91 / 2
Radius ≈ 25.46 inches
Area of circle = π * (25.46)^2
Area of circle ≈ 3.14 * 647.86
Area of circle ≈ 2035.00 in^2
Area of square = Side^2
Area of square = 36^2
Area of square = 1296 in^2
Area of shaded portion = Area of square - Area of circle
Area of shaded portion = 1296 - 2035
Area of shaded portion ≈ 739.00 in^2
Therefore, the correct answer is not listed, the closest option is 1,276.00 in^2.