SOLUTION: 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

Algebra ->  Algebra  -> Circles -> SOLUTION: 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      Log On

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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 cm.
Answer by ankor@dixie-net.com(7696) About Me  (Show Source):
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: 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%28R%5E2+-+r%5E2%29
:
Given that R - r = 2; therefore:
R = (r+2)
;
Substitute (r+2) for r in the annulus formula:
A = pi%28%28r%2B2%29%5E2+-+r%5E2%29
FOIL
A = A = pi%28r%5E2+%2B+4r+%2B+4+-+r%5E2%29
:
A = pi%284r%2B4%29
:
A = 4pi%28r%2B1%29
:
r + 1 = A%2F%284pi%29
:
r = A%2F%284pi%29 - 1
:
Just substitute the value for A to find r (smaller radius)