Question

GCSE 995381

Answer 1

Answer:

$2.9 cm^2$

Step-by-step 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 = $\frac{1}{2}\times base \times height$

We know that,

$\sin \theta = \dfrac{P}{H}$

$\sin 30^\circ= \dfrac{P}{8}$

$P = \dfrac{8}{2}$

$P = 4\ cm$

And

$\cos \theta =\dfrac{B}{H}$

$\cos 30^\circ = \dfrac{B}{8}$

$B = \dfrac{8\times \sqrt{3}}{2}$

$B = 4\sqrt 3$

Area of sector = $\dfrac{\theta}{360^\circ}\times \pi r^2$

Area of sector =  $\dfrac{30^\circ}{360^\circ}\times \pi \times 8^2$

                        = 16.75 cm^2

Area of triangle = $\dfrac{1}{2} \times 4\sqrt 3 \times 4$

                          = 13.85 cm^2

Area of shaded region = 16.75 - 13.85

                                      = $2.9 cm^2$