Concentric Circles?

[donnagirl]

Three circles have the same center. Their radii measure 1, 2, and 3 respectively. If a point is chose at random in the interior of the largest circle, what is the probability that the point is also in the interior of the smalles circle?

I know the answer should be 1/9 but I can't figure out why.

 

[Mrspi]

Three circles have the same center. Their radii measure 1, 2, and 3 respectively. If a point is chose at random in the interior of the largest circle, what is the probability that the point is also in the interior of the smalles circle?

I know the answer should be 1/9 but I can't figure out why.

Write expressions for the areas of each of the three circles, using the formula

A = pi * r²

Leave the area of each circle in terms of pi.

Now, the probability that the chosen point is inside the smaller circle, given that it is inside the largest circle is

(area of smallest circle) / (area of largest circle)

Substitute the areas you have determined for each circle, and reduce the fraction.

(Hint: (3 pi) / (12 pi) reduces to 1/4)

 

[donnagirl]

Thanks so much Mrspi That makes much more sense!