The diagram shows a CD which has a radius of 6 cm. a) work out the circumference of the CD. Give your answer correct to three significant figures. CDs of this size are cut from rectangular sheets of plastic . Each sheet is 1 meter long and 50 cm wide.  b) Work out The greatest number of CDs which can be cut from one rectangular sheet.

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Question:

The diagram shows a CD which has a radius of 6 cm. a) work out the circumference of the CD. Give your answer correct to three significant figures. CDs of this size are cut from rectangular sheets of plastic . Each sheet is 1 meter long and 50 cm wide. 
b) Work out The greatest number of CDs which can be cut from one rectangular sheet.

Answers

Answer:13 CDs can be cut from 1 m x 50 cm sheetStep-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.

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