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
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