Question

The outer four small circle are tangent to the big circle and to the inner small circle in the center. All five small circles are congruent. Will Amtel shoot an arrow and hit somewhere in the large circle. What are odd that the arrow hit the shaded section?

Answer 1

For example you would set the radius of all the inner circles to 1. That means you can calculate the area of all 5 inner circles.
\[5 ( \pi r^2)\]with r = 1
This gives you 5 pi.

Then you can calculate the radius of the bigger circle.
The radius consists of 1 diameter and 1 radius of one of the smaller circles.
This means the radius is equal to 3.
Plug it into the formula for area to get you 9 pi.

Then you get the ratio of
\[5\pi/9\pi\]

Answer 2

This is what I got. (5:9) but it's not one of the multiple choices...

Here them are:
A) 5:4
B) 3:2
C) 5:2
D)1:1
E) 2:1

Answer 3

oh well i guess it's the 5:4

Answer 4

because of the 9 spots you have you can hit the inner circle 5 times of the entire 9
and then the rest 4/9 is the area leftover

Answer 5

Hmm it make sense. Thanks.