4MA0 Higher January 2017 Paper 3 Q22
22
Diagram NOT accurately drawn
The diagram shows a sector \(OAB\) of a circle, centre \(O\).
Angle \(AOB = 75^\circ\)
Length of arc \(AB = 7.2\) cm
Calculate the area of the sector.
Give your answer correct to 3 significant figures.
(4)
| Scheme | Marks |
|---|---|
| \(\dfrac{75}{360} \times \pi \times d\;(2r) = 7.2\) | M1 |
\(\dfrac{7.2 \times 360}{75 \times \pi}\) oe or \(\dfrac{7.2 \times 360}{75 \times 2 \times \pi}\) oe or \(d\) = 11(.0…) or \(r\) = 5.5(0…) | M1 |
\(\dfrac{75}{360} \times \pi \times \left(\dfrac{\text{“}11\text{”}}{2}\right)^2\) or \(\dfrac{75}{360} \times \pi \times \text{“}5.5\text{”}^2\) or \(\dfrac{75}{360} \times 95(.04...)\) | M1 |
| 19.8 | A1 |
| (4) | |
| (4 marks) |
Notes
M1: for a correct equation linking the angle and arc length
NB: 0.208(3… ) may be used in place of \(\dfrac{75}{360}\)
or 4.8 in place of \(\dfrac{360}{75}\)
M1: for a complete method to find the radius or diameter.
M1: dep on previous M1
A1: for answer in range 19.8 – 19.82