Edexcel IAL Mathematics P1.3.2 radian measure

Practise using radians to calculate arc lengths, sector areas, compound perimeters and areas in diagrams with circular parts.

Exam points

apply s=rθ to find arc lengths or include arcs in a total perimeter
use A=1/2r^2θ to find sectors, missing radii or combined areas
combine sector and triangle areas when a shape is made from circular and straight edges

[Maximum number: 7]

Figure 1

Figure 1 shows the plan view for the design of a stage.
The design consists of a sector OBC of a circle, with centre O, joined to two congruent triangles OAB and ODC.

Given that
- angle B O C=2.4 radians
- area of sector $B O C=40 \mathrm{~m}^{2}$
- AOD is a straight line of length 12.5 m

(a)

find the radius of the sector, giving your answer, in m , to 2 decimal places,

[ 2 ]

$A=\frac{1}{2}r^2\theta$ $40=\frac{1}{2}r^2\times2.4$

M1

$r=\sqrt{\frac{80}{2.4}}=5.77\text{ m}$

A1

(b)

find the size of angle AOB, in radians, to 2 decimal places.

Hence find

[ 1 ]

(c)

the total perimeter of the stage, giving your answer, in m , to one decimal place.

[ 4 ]

Arc length $=5.77\times2.4=13.848$

M1

$AB^2=6.25^2+5.77^2-2\times6.25\times5.77\cos(0.37)$ , so $AB=2.26\ldots$

M1

Perimeter $=12.5+2\times2.26\ldots+13.848$

ddM1

$=30.9\text{ m}$

A1

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P1.3.2 - Radian measure, question 1

Question (a)

Question (b)

Question (c)