Answer:
THE AMOUNT OF WASTE IS 61.8 square inches
THE PERCENT OF THE ORIGINAL STOCK THAT WAS WASTED IS 21.46
THE MATERIAL COST OF EACH CUT OUT CIRCLE IS $5.95
Explanation:
The area of the rectangle is:
[tex]A=LW[/tex]
Where L is the length, and W is the width.
[tex]\begin{gathered} A=24\times12 \\ =288in^2 \end{gathered}[/tex]
The area one of the cirlces is:
[tex]A=\pi r^2[/tex]
Where r is the radius, which measures 6 inches
[tex]\begin{gathered} A=6^2\pi \\ \\ =36\pi \\ \approx113.1 \end{gathered}[/tex]
The area of both circles is therefore, twice the area of one of the circles.
This is
[tex]\begin{gathered} 2(36\pi)=72\pi \\ \approx226.2 \end{gathered}[/tex]
THE AMOUNT OF WASTE IS:
[tex]\begin{gathered} 288-72\pi \\ \\ \approx61.8 \end{gathered}[/tex]
THE PERCENT OF THE ORIGINAL STOCK THAT WAS WASTED IS:
[tex]\begin{gathered} \frac{61.8}{288}\times100 \\ \\ \approx21.46\text{ percent} \end{gathered}[/tex]
The whole stock, which is 228 square inches cost $12
We want to find the cost of each cut out circle, that is 113.1
THE MATERIAL COST OF EACH CUT OUT CIRCLE IS:
[tex]\begin{gathered} \frac{12\times113.1}{228} \\ \\ \approx5.95 \end{gathered}[/tex]
The cost is $5.95
