Question

The area enclosed between the circumference of two concentric circle is 16πcm square and their radii are in the ratio 5 : 3. what is the area of the outer circle. (use π = 3.14)​

Answer 1

Answer:

Area of the outer circle = 78.5 $cm^2$

Step-by-step explanation:

The radii of two concentric circles are in the ratio 5 : 3.

If the radius of the outer circle is 5x

Then, the radius of the inner circle is 3x

According to the problem:

π$(5x)^2$ - π$(3x)^2$ = 16π

$=>(5x)^2 - (3x)^2 = 16$

$=>25x^2 - 9x^2 = 16$

$=>16x^2 = 16$

$=>x^2 = 1$

∴ $x = 1$

∴ The radius of the outer circle is 5 cm

And the radius of the inner circle is 3 cm.

∴ Area of the outer circle = π$5^2$ = 25x3.14 $cm^2$ = 78.5 $cm^2$

Answer 2

Answer:

Area of the outer circle = 78.5 cm^2cm

2

Step-by-step explanation:

The radii of two concentric circles are in the ratio 5 : 3.

If the radius of the outer circle is 5x

Then, the radius of the inner circle is 3x

According to the problem:

π(5x)^2(5x)

2

- π(3x)^2(3x)

2

= 16π

= > (5x)^2 - (3x)^2 = 16=>(5x)

2

−(3x)

2

=16

= > 25x^2 - 9x^2 = 16=>25x

2

−9x

2

=16

= > 16x^2 = 16=>16x

2

=16

= > x^2 = 1=>x

2

=1

∴ x = 1x=1

∴ The radius of the outer circle is 5 cm

And the radius of the inner circle is 3 cm.

∴ Area of the outer circle = π5^25

2

= 25x3.14 cm^2cm

2

= 78.5 cm^2cm

2