Question

The area of two sectors of two different circle of radii 7cm and 14cm are equal show that the ratio of angle at the centre is 4 :1​

plz help me today is my exam

Answer 1

Answer:

24147.2sq.cm way sector area and second sector area is1257.6 sq.cm

Answer 2

Answer with Step-by-step explanation:

Let

$r_1=7 cm$

$r_2=14 cm$

Area of one sector=$A_1=\frac{\theta}{360}\times \pi(7)^2$

Using the formula

Area of sector:$\frac{\theta}{360}\times \pi r^2$

Where r=Radius of circle

$\theta=$Central angle

Area of second sector,$A_2=\frac{\theta'}{360}\times \pi (14)^2$

According to question

$\frac{\theta}{360}\times \pi(7)^2=\frac{\theta'}{360}\times \pi (14)^2$

$\frac{\theta}{\theta'}=\frac{360\times\pi (14)^2}{360\times \pi (7)^2}=\frac{4}{1}$

$\frac{\theta}{\theta'}=4$

Hence, the ratio of angle at the centre=4:1

Hence, proved.

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