Question

three concentric circles daineter are in ratio 1:2:3 then find ratio of area​

Answer 1

Step-by-step explanation:

Given the diameters of concentric circles are in ratio 1:2:3 respectively.

Let the diameter of the concentric circles be s,2s,3s.

Radius of inner circle= r

1

=

2

s

Radius of middle circle = r

2

=

2

2s

=s

Radius of outer circle = r

3

=

2

3s

Area of first circle (first region ) = πr

1

2

=π

4

s

2

Area of second circle =πr

2

2

=πs

2

Area of third circle =πr

3

2

=π

4

9s

2

So Area of region enclosed between second and first circle =πr

2

2

−πr

1

2

=πs

2

−π

4

s

2

⇒

4

3πs

2

Area of region enclosed between third and second circle =πr

3

2

−πr

2

2

=π

4

9s

2

−πs

2

⇒

4

5πs

2

Ratio of area of three regions =π

4

s

2

:

4

3πs

2

:

4

5πs

2

Ratio =1:3:5