Higher June 2022 Paper 2R Q5
5 The diagram shows a shape made from a square \(ABCD\) and 4 identical semicircles.
Diagram NOT accurately drawn
As shown in the diagram, the semicircles have \(AB\), \(BC\), \(CD\) and \(DA\) as diameters.
The area of the square is 36 cm2
Calculate the total area of the shape.
Give your answer correct to one decimal place.
(4)
| Scheme | Marks |
|---|---|
| \(\sqrt{36}\;(= 6)\) or 6 or 6 × 6 | M1 |
eg \(\pi \times \left(\dfrac{[\text{their }6]}{2}\right)^2 \div 2\;\left(= 14.1\ldots\text{ or }4.5\pi\text{ or }\dfrac{9}{2}\pi\right)\) or \(\pi \times \left(\dfrac{[\text{their }6]}{2}\right)^2\;(= 28.2\ldots\text{ or }9\pi)\) | M1 |
| eg 4 × “14.1” (= 56.5… or \(18\pi\)) or 2 × “28.2” (= 56.5… or \(18\pi\)) | M1 |
| 92.5 | A1 |
| (4) | |
| (4 marks) |
Notes
M1: for method to find the length of the square – may be seen in later working
M1: for method to find the area of one semicircle or circle or the incorrect number of semicircles or circles provided correct area of circle formula is seen
for [their 6] allow any value if there is a clear implication this is their side length of square.
M1: ft dep on previous M1
for a complete method to find the total area of the semicircles
[if the pupil multiplies again and uses the incorrect number of circles or semicircles this mark is not awarded]
A1: accept 92.4 – 92.6
(not in terms of \(\pi\))