Jada cuts out a rectangular piece of paper that measures 5 inches by 4 inches. Han cuts out a paper sector of a circle with radius 5 inches, and calculates the arc length to be 2π inches. Whose paper is larger? Explain your reasoning.
Can't figure this without knowing the arc length......
Formula for arc length =
arc length = r θ where θ is in radians
So we have
2pi = 5 θ solve for θ and we have that
θ = [ 2 pi ] / 5
The area of the sector =
(1/2) r^2 θ = (1/2)(5^2) (2pi) / 5 = 5 pi in^2 ≈ 15.7 in ^2
The rectangular shape has more area = (5 * 4) = 20 in ^2