Math, asked by ishanaik1904, 1 month ago

the area envlosed between two concentric circles is 808.5cm2 the circumference of the outer circle is 242cm.find radius of the inner circle and width of the ring​

Answers

Answered by tennetiraj86
3

Step-by-step explanation:

Given:-

the area enclosed between two concentric circles is 808.5cm2 the circumference of the outer circle is 242cm.

To find:-

find radius of the inner circle and width of the ring

Solution:-

Area enclosed between two concentric circles =

Area of the circular path

=Area of the ring = 808.5 cm^2

Let the outer radius be 'R' units

and Let the inner radius be 'r' units

Area of the ring =π(R+r)(R-r) sq.units or

π(R^2-r^2) sq.units

Therefore,π(R+r)(R-r) = 808.5 cm^2 -------(1)

The circumference of the outer circle = 242 cm

Circumference of a circle with the radius 'R' units

=>2πR units

=>2πR = 242

=>πR = 242/2

=>πR = 121

=>(22/7)×R = 121

=>R = 121×7/22

=>R = 11×7/2

=>R = 77/2 cm or 38.5 cm

Outer radius of the circle = 38.5 cm

On Substituting the value of R in (1) then

=>π[(38.5)^2-r^2]=808.5

=>(22/7)[(1482.25)-r^2] = 808.5

=>1482.25 - r^2 = 808.5×7/22

=>1482.25-r^2 = 5659.5/22

=>1482.25-r^2 = 257.25

=>-r^2 = 257.25-1482.25

=>-r^2 = -1225

=>r^2 = 1225

=>r^2 = 35^2

=>r = 35 cm

Inner radius of the circle = 35 cm

We have

Outer radius = 38.5 cm

Inner radius = 35 cm

Width of the circular path (w)

=Outer radius- Inner radius.

=>W = R-r

=>W= 38.5-35

=>W = 3.5 cm

Width = 3.5 cm

Answer:-

Width of the circular path or of the ring = 3.5 cm

Used formulae:-

1) If the outer radius be 'R' units and the inner radius are 'r' units then Area of the ring

=π(R+r)(R-r) sq.units or π(R^2-r^2) sq.units

2)Width of the ring (W)=R-r

3)Circumference of the circle=2πr units

Where π=22/7

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