Foundation June 2018 Paper 2 Q21
21 This shape consists of three semicircles.
OP = OQ.
The length of PQ is \(4x\) cm.
Show that the area, in cm\(^2\), of the whole shape is \(3\pi x^2\). [5]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| Radius C is \(2x\) Or radius A or B is \(x\) | B1 | A and B are the small semicircles C is the large semicircle May be indicated on the diagram | |
| Area C = \(\dfrac{\pi \times (2x)^2}{2}\) oe | M1 | ||
| \(= 2\pi x^2\) | A1 | ||
| Area A or B = \(\dfrac{\pi \times x^2}{2}\) oe | M1 | or Area A + B = \(\pi x^2\) oe | \(\pi x^2\) must result from combining area A and area B |
| Area = \(2\pi x^2 + \dfrac{\pi x^2}{2} + \dfrac{\pi x^2}{2} = 3\pi x^2\) | A1 | or Area = \(2\pi x^2 + \pi x^2 = 3\pi x^2\) | Addition must be seen with no errors or omissions but condone equivalent expressions for \(2\pi x^2\), \(\dfrac{\pi x^2}{2}\), \(\pi x^2\) |