Foundation November 2017 Unit 2 Q16
16. \(AB\) is the diameter of a circle, centre \(O\), with radius \(OA\) = 4·2 cm.
\(ABCD\) is a square.
Diagram not drawn to scale
Calculate the area of the shaded region.
You must show all your working. [5]
| Scheme | Marks | Comments |
|---|---|---|
| (Area of the circle =) π × 4·22 OR (Area of semi-circle =) \(\dfrac{\pi \times 4{\cdot}2^2}{2}\) | M1 | |
| = 55·4(…)(cm2) OR 27·7(…)(cm2) | A1 | Accept an answer that rounds to 55·4 cm2 OR an answer that rounds to 27·7 cm2 |
| (Side of square or Diameter =) 8·4 (cm). | B1 | Look at diagram. May be seen in further work. |
| (Area of the square = ) = 70·56(cm2) | B1 | Implies previous B1. Allow 70·6. |
| (Shaded area = 70·56 − \(\dfrac{55{\cdot}4}{2}\) ) = 42·85 (cm2) | B1 | F.T. ‘their area of square’− ‘their area of semi circle.’ (Allow tolerance of ±0·05 for the subtraction.) |