Question

11). A semicirde is divided into two sectors, whose angles are
in the ratio 2:3. Find the ratio of their singles areas.​

Answer 1

Answer:

answer for the given problem is given

Answer 2

 Answer -

A1 : A2 = 2 : 3

Explanation -

Let r be the radius of semicircle.

Let x be some common multiple such that small sector has angle θ1=2x and large sector has angle θ2=3x.

We know that semicircle measures 180°.

2x + 3x = 180°

5x = 180°

x = 36°

Measure of angles -

θ1 = 2x = 2×20 = 40°

θ2 = 3x = 3×20 = 60°

Area of small sector -

A1 = πr^2.θ1/360°

A1 = πr^2 × 40/360

Area of large sector -  

A2 = πr^2.θ2/360°

A2 = πr^2 × 60/360

Ratio of areas is -

A1/A2 = (πr^2×40/360) / (πr^2×60/360)

A1/A2 = 2/3

Therefore, ratio of areas of two sectors is 2:3