M07.C-G.2.2.1
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?
(π = 3.14)
(5 points)
Group of answer choices
150.72 in2
192.00 in2
1,152.00 in2
1,808.64 in2
To find the area of the cloth that was cut from the square, we need to find the area of the circle.
The square has a side length of 48 inches, so its area is 48 * 48 = 2304 square inches.
The circle's diameter is equal to the side length of the square, which is 48 inches. The radius of the circle is half of the diameter, so the radius is 48 / 2 = 24 inches.
The area of the circle is π * radius^2 = 3.14 * 24^2 = 3.14 * 576 = 1809.6 square inches.
Therefore, the area of the cloth that was cut from the square is 1809.6 square inches.
Answer: 1,809.6 in2