Higher June 2024 Paper 2R Q5
5 The diagram shows the design for a badge, which will be made using wire.
The design is a circle inside a square \(ABCD\)
Diagram NOT accurately drawn
The circle touches the square at the points \(E\), \(F\), \(G\) and \(H\)
The area of the square is 81 cm²
Calculate the total length of wire that will be needed to make the square and the circle.
Give your answer correct to 3 significant figures.
(4)
| Scheme | Marks |
|---|---|
| \(\sqrt{81}\) (= 9) or 9 or 9 × 9 (= 81) | M1 |
| 4 × “9” (= 36) oe | M1 |
| eg \(\pi \times\) “9” (= 28.2(743...) or \(9\pi\)) | M1 |
| Working not required, so correct answer scores full marks (unless from obvious incorrect working) Answer: 64.3 | A1 |
| (4) | |
| (4 marks) |
Notes
M1: for method to find the length of the side of the square (may be seen on the diagram)
M1: for the perimeter of the square
(the first M mark can be implied by 36)
M1: for a correct expression for the circumference for using \(2\pi r\) or \(\pi D\)
(the first M mark can be implied by 28.2(743…) rounded or truncated to 1 dp or by \(9\pi\))
A1: accept 64.26 – 64.3