Foundation November 2023 Unit 2 Q20
20. The diagram shows two circles that fit in a rectangle.
The centre of the small circle is directly below the centre of the large circle.
The diameter of the small circle is 8 cm.
The radius of the large circle is 2 cm greater than the radius of the small circle.
Diagram not drawn to scale
Calculate the total area of the shaded parts of the rectangle. [5]
| Scheme | Marks | Comments |
|---|---|---|
| (Radius of smaller circle =) 4 (cm) AND (Radius of larger circle = 4 + 2 =) 6 (cm) | B1 | Check diagram for answers. May be seen or implied in later working. |
| (Width of rectangle = 8 + 2 + 2 or 6 + 6 = ) 12 (cm) AND (Length of rectangle = 8 + 2 + 2 + 8 or 6 + 6 + 8 = ) 20 (cm) | B1 | May be seen or implied in later working. Implies previous B1. FT 2 × ‘their 6’. FT 8 + 2 × ‘their 6’. |
| (Shaded area =) 20 × 12 – π × 42 – π × 62 or (12 × 12) – π × 62 + (12 × 8) – π × 42 | M2 | FT ‘their 12(cm)’ and ‘their 20(cm)’ for a possible M2 and possible A1. FT ‘their 4(cm)’ and ‘their 6(cm)’ for a possible M2 A0. If a 12 × 12 square and 12 × 8 rectangle used, the previous B1 is implied. Award M1A0 for sight of any of the following (FT ‘their 12(cm)’, ‘their 20(cm)’, ‘their 4(cm)’ and ‘their 6(cm)’):
|
| Accept answers in the range 76·6 to 76·72 (cm2) or 240 – 52π (cm2) | A1 | Allow 77 (cm2) from correct working. |