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.
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