Question

A circular plaque of diameter 6cm is cut from a square piece of metal with side length 6cm.What percentage of the metal is wasted?

Answer 1

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

`\begin{gathered} =\pi*3^2 \\ =9\pi\; cm^2 \end{gathered}`

Therefore:

Area of the Shaded Portion=Area of Metal Piece-Area of circular Plaque

`=(36-9\pi)cm^2`

The percentage of metal that was wasted will then be:

`\begin{gathered} =\frac{\text{Area of the Shaded Portion}}{\text{Area of the Metal Piece}}*100 \\ =\frac{\text{3}6-9\pi}{\text{3}6}*100 \\ =\frac{\text{3}6-9(3.14)}{\text{3}6}*100 \\ =\frac{\text{7}.74}{\text{3}6}*100 \\ =21.5\% \end{gathered}`

The percentage of metal that is wasted is approximately 21.5%.