Given a square piece of metal of side length 6cm
If a circular plaque of diameter 6cm is cut from the metal piece, the area wasted is the shaded area in the diagram below:
Total Area of the Metal Piece = 6 x 6 = 36 square cm
Area of the Circular Plaque
[tex]\begin{gathered} =\pi\times3^2 \\ =9\pi\; cm^2 \end{gathered}[/tex]Therefore:
Area of the Shaded Portion=Area of Metal Piece-Area of circular Plaque
[tex]=(36-9\pi)cm^2[/tex]The percentage of metal that was wasted will then be:
[tex]\begin{gathered} =\frac{\text{Area of the Shaded Portion}}{\text{Area of the Metal Piece}}\times100 \\ =\frac{\text{3}6-9\pi}{\text{3}6}\times100 \\ =\frac{\text{3}6-9(3.14)}{\text{3}6}\times100 \\ =\frac{\text{7}.74}{\text{3}6}\times100 \\ =21.5\% \end{gathered}[/tex]The percentage of metal that is wasted is approximately 21.5%.
