A circle is cut from a square piece of cloth, as shown:
A square, one side labeled as 48 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? 150.72 in2
192.00 in2
1,152.00 in2
1,808.64 in2
To find how many square inches of cloth are cut from the square, we first need to calculate the area of the circle. The diameter of the circle is equal to the side length of the square, which is 48 inches.
The radius of the circle is half of the diameter, so it is 24 inches.
Now, we can calculate the area of the circle using the formula A = πr^2, where A is the area and r is the radius.
A = π(24)^2
A = π(576)
A = 576π
Next, we need to calculate the area of the square. The formula for the area of a square is side length squared.
A = 48^2
A = 2304
Since the circle touches all sides of the square, the shaded portion outside the circle is the difference between the area of the square and the area of the circle.
Shaded area = Area of square - Area of circle
Shaded area = 2304 - 576π
Shaded area = 2304 - 576(3.14159)
Shaded area ≈ 150.72 in^2
Therefore, the answer is 150.72 in^2.