Kiran cuts out a square piece of paper with side length 6 inches. Mai cuts out a paper sector of a circle with radius 6 inches, and calculates the arc length to be inches. Whose paper is larger? Explain or show your reasoning.

Arc length doesn’t matter. Area does.

Area of a square: bh = 6x6 = 36 inches squared

Area of a circle: 3.14(r^2) = 3.14(36)= 113 inches squared

Mai’s paper is much larger.

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ap8997154 ap8997154 · Answer 2 · 2022-05-25T11:37:44+02:00

A circle is a curve sketched out by a point moving in a plane. The area of the circular paper is more than the area of the square.

What is a circle?

A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.

The arc length of radius 6 inches is equal to,

Length of the Arc of a quarter = 2πr×(1/4) = 2×π×6×0.25 =0.9448 inches

The area of the circular paper = πr² = π×6×6 = 113.097²

The area of the square with a side of 6 inches = 36 in²

Therefore, the area of the circular paper is more than the area of the square.

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