Foundation November 2018 Paper 1 Q26
26 The diagram shows a square \(ABCD\) with sides of length 20 cm.
It also shows a semicircle and an arc of a circle.
\(AB\) is the diameter of the semicircle.
\(AC\) is an arc of a circle with centre \(B\).
Show that \(\dfrac{\text{area of shaded region}}{\text{area of square}} = \dfrac{\pi}{8}\) (4)
| Answer | Mark | Mark scheme |
|---|---|---|
| shown | C1 | for method to find area of semicircle, eg \(\pi \times 10^2 \div 2\ (= 50\pi)\) |
| C1 | for method to find area of quarter circle, for \(\pi \times 20^2 \div 4\ (= 100\pi)\) | |
| C1 | for a complete method to find area shaded and area of square, eg \(\pi \times 20^2 \div 4 - \pi \times 10^2 \div 2\) and \(20 \times 20\) | |
| C1 | fully correct working leading to \(\dfrac{\pi}{8}\) |
Additional guidance
Can award first 3 marks if a value for \(\pi\) is used
Working out to find the area of the shaded region must be shown