Question

the area enclosed between the circumference of two concentric circles is 16 pi CM sq and their radii are in ratio 5:3 what is the area of the outer circle? ( use the pi = 3.14)

Answer 1

The length of the Chord is 24. As it is Tangent to small circle, the length of from edge of the chord to mid point of the chord is 12.

Let say radius of inner circle is r and of big circle is R. Then according to hypotenuse theory, r^2 +144=R^2.

Now coming to difference in area =pi*(R^2-r^2) =pi*144=144pi

Answer 2

ro2 - ri 2= 16
divide by ro2 both sides

= 1 - (ri/ro)^2 =16/ro^2
= 1 - 9/25 = 16 /ro^2
= 16/9 = 16/ro^2
ro=3

area of outer = pie. 9