A circle is cut from a square piece of cloth, as shown: A square, one side labeled as 34 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) 907.46 in2 986.32 in2 1,024.00 in2 1,156.00 in2

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16-06-2018
Mathematics

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A circle is cut from a square piece of cloth, as shown: A square, one side labeled as 34 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) 907.46 in2 986.32 in2 1,024.00 in2 1,156.00 in2

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AL2006 AL2006 · Answer 1 · 2018-06-16T06:21:53+02:00

Please look at the picture that you mentioned in the question
but decided not to let us see.

The circle is inside the square, and touches all sides of the square.
You'll notice that the diameter of the circle is the same length as
each side of the square, and the radius is 1/2 as long as a side.

Area of a circle = π R²

The radius of this circle is 17 inches . . . 1/2 the side of the square.

Area of the circle = π (17²) = 907.46 in² .

That's the area of the circle.

The other 258.5 in² of cloth is discarded after it's trimmed away.

astha8579 astha8579 · Answer 2 · 2022-01-27T14:00:56+01:00

You can use the fact that the cloth piece cut is circular and its area will give the area of cloth piece that is cut from the square piece of cloth.

The area of the cloth piece cut from the square is:

Option A: 907.46 square inches

How to find the property of circle which is fully fitted inside a square?

Since the circle is fully fitted, its longest chord which is diameter must be touching both the bottom side and top side, and both the left and right side. The opposite side of squares will serve as two tangents on the opposite ends of diameters of that circle. Thus, being perpendicular to other two pair of sides, we have the length of the diameter of the circle which is inside the square is equal to the length of side of square.

How to find the area of the cloth piece cut from the square?

Since the diameter of the circular cut piece is of the same length as that of the side of the square,thus, we have:

diameter of circle = 34 inches.

Thus, radius of circle = diameter/2 = 17 inches.

Thus, area of that circular cloth piece is obtained by:

[tex]A = \pi r^2\\A = 3.14 \times 17\\A = 907.46 \: \rm in^2[/tex]

Thus,

The area of the cloth piece cut from the square is:

Option A: 907.46 square inches

Learn more about radius and area of circle here:

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