Question 207289
: Consider an area of cm2 bounded by two concentric circles ( the figure is called an annulus). Determine the radius of the inner circle ( in units of cm) if the outer and the inner diameters of the of the annulus differ by 2 
:
The area of an annulus formula
A = {{{pi(R^2 - r^2)}}}
:
Given that R - r = 2; therefore:
R = (r+2)
;
Substitute (r+2) for r in the annulus formula:
A = {{{pi((r+2)^2 - r^2)}}}
FOIL
A = A = {{{pi(r^2 + 4r + 4 - r^2)}}}
:
A = {{{pi(4r+4)}}}
:
A = {{{4pi(r+1)}}}
:
r + 1 = {{{A/(4pi)}}}
:
r = {{{A/(4pi)}}} - 1
:
Just substitute the value for A to find r (smaller radius)