SOLUTION: Diagram of circle with outer edge shaded. The outer circle has diameter 8 inches. The area of the shaded ring is equal to the are of the inner, non-shaded circle. What is the radi

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Question 909337: Diagram of circle with outer edge shaded. The outer circle has diameter 8 inches. The area of the shaded ring is equal to the are of the inner, non-shaded circle. What is the radius of the inner circle? Express your answer as a decimal to the nearest tenth.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39618)   (Show Source): You can put this solution on YOUR website!
R, radius of the outer circle
r, radius of the inner (smaller) circle
inches
r is unknown.

Area of outer circle, ;
Area of smaller inner circle, ;
Difference in areas is the area of your shaded ring surrounding the inner circle, .

According to the description, .
You want to solve for r.

STEPS
Divide both members by pi.



, and you might want to rationalize the denominator.

----the symbolic answer.

Substitute for R and evaluate r.
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

Diagram of circle with outer edge shaded. The outer circle has diameter 8 inches. The area of the shaded ring is equal to the are of the inner, non-shaded circle. What is the radius of the inner circle? Express your answer as a decimal to the nearest tenth.


Let radius of smaller, non-shaded, inner circle, be r

Then area of smaller, non-shaded circle is: 

Now, since the area of the smaller, non-shaded circle and the shaded area are equal, then

the area of the smaller, non-shaded circle and the shaded region = , or 

Area of larger circle is: , or 

Therefore, we get: 

 ------ Factoring out GCF, 

  

r, or radius of smaller, non-shaded, inner circle = , or , or  ≈  inches  

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