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Marty is making a mosaic piece of art using pre-cut pieces of tile. He is at the store looking at pieces shaped like the picture below.

 

Marty wants to fill his canvas space of 4 feet x 5 feet. He already has 83 pieces of 2 inch x 5 inch, rectangular tile left over from the kitchen remodel that he plans to use in the mosaic. Assuming that all of the wedge-shaped tiles are 40°sectors cut from a circle with a radius of 3 inches, what is the maximum number of pieces he should buy to complete his project?

Use 3.14 for π.

 

http://prntscr.com/mpaynt

 Feb 24, 2019
edited by Melody  Feb 24, 2019
 #1
avatar+98060 
+2

4ft x 5 ft =    48 in * 60 in =  2880 in^2

 

He already has enough tiles to fill  83 (2 * 5) = 83 * 10  =  830 in^2

 

So....the remaining area left to fill is   2880 - 830  =  2050 in^2   left to fil

 

Each piece of the wedge-shaped tile has an area of  3.14 (3)^2 ( 40/360) = 3.14 in^2

 

So....the number of pieces he needs =   ceiling  [ 2050 / 3.14 ]  = 653 pieces 

 

 

cool cool cool

 Feb 24, 2019
edited by CPhill  Feb 24, 2019
 #2
avatar+37 
+1

Thank you!

JoseyP  Feb 24, 2019

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