+0  
 
+1
137
3
avatar+956 

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.

 May 15, 2020
edited by GAMEMASTERX40  May 15, 2020
 #1
avatar+111455 
+1

Can't figure this without knowing the arc length......

 

 

cool cool cool

 May 15, 2020
 #2
avatar+956 
+1

Oopsie! Sorry, CPhill I did not see that mistake. I fixed it now and the arc length should be 2π inches. 

GAMEMASTERX40  May 15, 2020
 #3
avatar+111455 
+2

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

 

 

 

cool cool cool

 May 15, 2020

58 Online Users

avatar
avatar
avatar