Answer:
13 CDs can be cut from 1 m x 50 cm sheet
Step-by-step explanation:
a) The circunference of the CD is represented by the following formula:
[tex]x^{2}+y^{2} = 36\,cm^{2}[/tex] (1)
Where:
[tex]x[/tex] - Horizontal position, measured in centimeters.
[tex]y[/tex] - Vertical position, measured in centimeters.
Now, we proceed to present a representation of the CD.
b) The area of a CD is represented by the following formula:
[tex]A_{CD} = \pi\cdot r^{2}[/tex] (2)
Where:
[tex]A_{CD}[/tex] - Area of the CD, measured in square centimeters.
[tex]r[/tex] - Radius, measured in centimeters.
If we know that [tex]r = 6\,cm[/tex], then the area of a CD is:
[tex]A_{CD} = \pi\cdot (6\,cm)^{2}[/tex]
[tex]A_{CD} = 113.097\,cm^{2}[/tex]
The area of the sheet is represented by this expression:
[tex]A_{s} = w\cdot l[/tex] (3)
Where:
[tex]A_{s}[/tex] - Area of the sheet, measured in square centimeters.
[tex]w[/tex] - Width of the sheet, measured in centimeters.
[tex]l[/tex] - Length of the sheet, measured in centimeters.
If we know that [tex]w = 50\,cm[/tex] and [tex]l = 100\,cm[/tex], the area of the sheet is:
[tex]A_{s} = (100\,cm)\cdot (50\,cm)[/tex]
[tex]A_{s} = 1500\,cm^{2}[/tex]
Now we divide the area of the sheet by the area of the CD:
[tex]n = \frac{A_{s}}{A_{CD}}[/tex] (4)
[tex]n = \frac{1500\,cm^{2}}{113.097\,cm^{2}}[/tex]
[tex]n = 13.263[/tex]
The maximum number of CD is the integer that is closer to this result. Therefore, 13 CDs can be cut from 1 m x 50 cm sheet.
