Question

GCSE 995381

IGCSE PASTE
NOT TO
SCALE
Past Papers
8 cm
30°
A
OAB is the sector of a circle, centre 0, with radius 8 cm and sector angle 30°.
BC is perpendicular to OA.
Calculate the area of the region shaded on the diagram.

Answer 1

`2.9 cm^2`

Explanation:

Given,

Angle of sector = 30°

Radius of circle, r = 8 cm

Area of the shaded region, A =?

The diagram is attached below.

Now,

Area of shaded region = Area of sector - Area of triangle

Area of triangle =
`(1)/(2)* base * height`

We know that,

`\sin \theta = (P)/(H)`

`\sin 30^\circ= (P)/(8)`

`P = (8)/(2)`

`P = 4\ cm`

And

`\cos \theta =(B)/(H)`

`\cos 30^\circ = (B)/(8)`

`B = (8* √(3))/(2)`

`B = 4\sqrt 3`

Area of sector =
`(\theta)/(360^\circ)* \pi r^2`

Area of sector =
`(30^\circ)/(360^\circ)* \pi * 8^2`

= 16.75 cm^2

Area of triangle =
`(1)/(2) * 4\sqrt 3 * 4`

= 13.85 cm^2

Area of shaded region = 16.75 - 13.85

=
`2.9 cm^2`