two circles touching int. at A , area of shaded region = 5500 cm2 MN=7 cm Find sum of radii .the fig is two circles one big and one small touching each other internally the shadded region is...
two circles touching int. at A , area of shaded region = 5500 cm2
Find sum of radii .
the fig is two circles
one big and one small touching each other internally
the shadded region is the remaining part of bigger circle
By data the two are is touching internally. The area of theregion between the bigger and smaller circle is 5500 cm^2. The distance between the centres of the circles is 7cm.
Therefore the distance between the centres of the circles = r2-r1, the difference of the radii of the outer and inner circles.
So r2-r1 = 7...(1)
Also the difference in areas of the outer and inner circles = pr2^2-pir1^2 which is 5500 cm^2 by data.
=> pir2^2-pir1^2 = 5500..(2).
Therefore from two we get (r^2^2-r1^2) = 5500 /pi = 1750.70.
=> r2^2-r1^2 = 1750.70.
=> (r1+r1)(r2-r1) = 1750.70.....(3).
From r1-r1 = 7. We substitute r1-r1 = 7 in (3) and get:e( r2+r1)*7 = 1750.7044.
=> r2+r1 = 1750.70/7 = 250.1006....(4).
(1)+(2): 2r2 = 7+250.1006. So r2 = 257.1006/2 = 128.5503 cm
(1) - (2): 2r1 = 250.1006-7 = 243.1006. So r1 = 243.1006/2 121.5503 cm.
Therefore the radius r2 of the outer circle is r2 = 121.5503 cm
The radius of the inner circle is r1 = 121.5503 cm.