Higher June 2024 Paper 1 Q15
15 \(OAB\) is a sector of a circle with centre \(O\) and radius 6 cm.
The length of the arc \(AB\) is \(5\pi\) cm.
Work out, in terms of \(\pi\), the area of the sector.
Give your answer in its simplest form. (4)
| Answer | Mark | Mark scheme |
|---|---|---|
| \(15\pi\) | P2 | for process to find size of the angle eg \(\dfrac{5\pi \times 360}{2 \times \pi \times 6}\) oe (= 150) or for working with proportion eg \(\dfrac{5\pi}{12\pi}\ \left(= \dfrac{5}{12}\right)\) or \(\dfrac{12\pi}{5\pi}\ \left(= \dfrac{12}{5}\right)\) |
| (P1 | for a first step eg \(\dfrac{x}{360} \times 2 \times \pi \times 6 = 5\pi\)) | |
| P1 | (dep on P2) for process to find the area eg \(\dfrac{\text{``}150\text{''}}{360} \times \pi \times 6^2\) or \(\dfrac{5\pi}{12\pi} \times \pi \times 6^2\) | |
| A1 | cao |