a) $2.58 of material has been wasted.
b) 21.52% of that material has been wasted.
c) So each circle costs $4.71
1) Since the plate are going to be cut to make 2 identical circles,
a) The Amount of waste
$ 12 each piece of stock
The radius of each circle is 6 inches
The area of both circles: 2[π(6)²] = 2π36 = 72π in² =226.19 in²
The area of the rectangle: 24 x 12 =288 in
Calculate the waste:
288-226=62
$12------------------------ 288 inches
x-----------------------------62
288x =744
x=$2.58
$2.58 of material has been wasted.
b) Let's consider a similar proportion to calculate that:
100%------------288 inches
y -----------------62 inches
y=21.52% of that material has been wasted.
c) Since each circle has an area of 36π inches ≅ 113 inches
Then, we can set another proportion
$12------------288
z---------------113
z=1356 ÷ 288 z ≅ 4.71
So each circle costs $4.71