A uniform circular track is the area bounded by two concentric circles. If the area of the track is 1144 m² and its width is 14 m, find the diameters of the two circles.
Answers
Diameter of outer circle = 40 m
Diameter of inner circle = 12 m
Explanation:
Area of a circle = Pi * r^2
Area of the track = 1144 sq. m.
Width of track = 14 m
Radius of outer circle = R
Radius of inner circle = r = R-14 m
Area of outer circle - area of inner circle = (Pi * R^2) - (Pi * (R-14)^2)
= 22 / 7 * (R^2 - (R^2 + 14^2 - 28R))
= 22 / 7 * (R^2 - R^2 - 14^2 + 28 R)
= 22 / 7 * 14 * 2 (R - 7)
= 22 * 4 (R - 7)
Since we know area of track, we get 22 * 4 * (R-7) = 1144
R-7 = 1144/(88) = 13
R = 20 m
Radius of outer circle = 20 m, so diameter = 40 m
Radius of inner circle = 6 m, so diameter = 12 m
Answer:
Q1. Let the radii of inner circle be x and Thor outer circle be x+14. WKT,
area of the track =pi(R^2-r^2) 1144=22/7[(x+14)^2-(x)^2]
1144*7/22-[x^2+14^2+2(x)(14)]-x^2 364 x^2+196+28x-x^2
364-196+28x
364-196-28x
168=28x
168/28=x
x=6
Therefore,radius of inner circle =6m radius of outer circle=20m Diameter of inner circle =12m Diameter of outer circle =40m