19M.1.AHL.TZ1.H_3

pestleMathematicsAAHLPaper 119M· sl-3-4-circle-radians-arcs-sectorssource ↗

A sector of a circle with radius $r$ cm , where $r$ > 0, is shown on the following diagram.
The sector has an angle of 1 radian at the centre.

Let the area of the sector be $A$ cm² and the perimeter be $P$ cm. Given that $A = P$ , find the value of $r$ .

Markscheme / solution

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

$A = P$

use of the correct formula for area and arc length (M1)

perimeter is $r\theta + 2r$ (A1)

Note: A1 independent of previous M1.

$\frac{1}{2}{r^2}\left( 1 \right) = r\left( 1 \right) + 2r$ A1

${r^2} - 6r = 0$

$r = 6$ (as $r$ > 0) A1

Note: Do not award final A1 if $r = 0$ is included.

[4 marks]

Examiners’ report

[N/A]