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

What is the ratio of the area of sector ABC to the area of sector DBE?-example-1
User Danjuggler
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2 Answers

3 votes

Answer:

4/3

Explanation:

User Jonesopolis
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4 votes

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 =
(2r^(2)*\ (\pi)/(180) beta)/(3/2 r^(2)*\ (\pi)/(180)beta)

= 4/3