SOLUTION: The area of the shaded region represents one-third of the total, What is the size of the radii such that this is possible? The radius of the whole circle is 12cm while the sha

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Question 1182220: The area of the shaded region represents one-third of the total, What is the
size of the radii such that this is possible?
The radius of the whole circle is 12cm while the shaded region is a ring in
the middle with a small not shaded circle in the middle.
Found 4 solutions by ankor@dixie-net.com, Edwin McCravy, greenestamps, MathTherapy:
Answer by ankor@dixie-net.com(22740)   (Show Source): You can put this solution on YOUR website!
he area of the shaded region represents one-third of the total, What is the size of the radii such that this is possible?
The radius of the whole circle is 12cm while the shaded region is a ring in the middle with a small not shaded circle in the middle.
;
Find 1/3 of the area of the whole circle
*
let R = radius to the outer ring
let r = radius to the inner ring
:


divide both sides by pi

graph this equation
Where R is on the y axis, r is on the x axis
first integer solution
R = 8, r = 4
see if that works

201.062 - 50.265 = 150.797
The radii of 8 and 4 make this possible
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!


Since the green area is 1/3 of the area of the outer circle, the area of the
inner circle is 2/3 of the area of the outer circle.

Using the area of a circle formula ,

















So the radius of the inner circle must be 4√6 or about 9.8 cm.

Edwin
Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!


The area of the ring is 1/3 the area of the circle with radius 12cm, so the area of the inner circle is 2/3 the area of the large circle.

Since the ratio of the areas of the two circles is 2:3, the ratio of the radii of the two circles is the square root of that ratio -- sqrt(2):sqrt(3).

ANSWER: The radius of the inner circle is

= 9.7979..., or 9.78 to 2 decimal places.
Answer by MathTherapy(10555)   (Show Source): You can put this solution on YOUR website!

The area of the shaded region represents one-third of the total, What is the
size of the radii such that this is possible?
The radius of the whole circle is 12cm while the shaded region is a ring in
the middle with a small not shaded circle in the middle. 
Area of larger circle: 

With radius of smaller circle being r, we get the area of the smaller circle as: 

Area of shaded region: 

Area of shaded region is also  the area of the larger circle.

We then get: 

           

                     

Since this is a measurement, CORRECT answer is , as the negative value for the radius is IGNORED. 

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