Circles
Problem situations in perimeter and area at this level will include calculations involving a circle or part of a circle.
Question
The window at the top of a door is in the shape of a semicircle.
The door is \(0.8m\) wide.
If the glass in the window is broken what area of glass is needed to replace the window?
We have been told that the window is a semicircle.
Making a rough sketch of the whole shape is usually helpful.
The width of the door is the same as the diameter of the semicircle, so we can use half of this distance as the radius.
\(Radius = \frac{1}{2}d\)
\(= \frac{1}{2} \times 0.8\)
\(= 0.4m\)
Area of circle \(=\pi r^{2} \)
\(=3.14\times\,0.4\,\times0.4 \)
\( =0.5024\,\,m^{2} \)
Area of semicircle \(=\frac{1}{2}\,\times0.5024=0.25\,\,m^{2}\,\,\) (to 2 decimal places)
