Question

What is the ratio of the area of sector ABC to the area of sector DBE?

Answer 1

The area of sector ABC is = x.  The area of sector DBE is = y.  The ratio of the area ABC to the area of DBE = x/y (x over y OR x divided by y)

Answer 2

We have to find the" ratio of the area of sector ABC to the area of sector DBE".

Now,

the general formula for the area of sector is

Area of sector= 1/2 r²θ

where r is the radius and θ is the central angle in radian.

180°= π rad

1° = π/180 rad

For sector ABC, area= 1/2 (2r)²(β°)

= 1/2 *4r²*(π/180 β)

= 2r²(π/180 β)

For sector DBE, area= 1/2 (r)²(3β°)

= 1/2 *r²*3(π/180 β)

= 3/2 r²(π/180 β)

Now ratio,

Area of sector ABC/Area of sector DBE =$\frac{2r^{2}*\ \frac{\pi}{180} beta}{3/2 r^{2}*\ \frac{\pi}{180}beta}$

= 4/3