SOLUTION: The diagram shows that x is the radius of the large circle and the diameter of the small circle. Write the ratio of the area of the large circle to the area of the area of the smal

Algebra ->  Circles -> SOLUTION: The diagram shows that x is the radius of the large circle and the diameter of the small circle. Write the ratio of the area of the large circle to the area of the area of the smal      Log On


   

Question 1020975: The diagram shows that x is the radius of the large circle and the diameter of the small circle. Write the ratio of the area of the large circle to the area of the area of the small circle. Simplify the expression.
http://i410.photobucket.com/albums/pp186/anentities/2E1E41E8-C61B-46BB-BA25-4AF907D931D7_zps3qqjpshu.jpg
Is a picture of the diagram and question. I know that the answer is 4, but I have absolutely no clue how to get to it. Thank you very much for answering! :)
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
the area of the circle is A=r%5E2%2Api
if x is the radius of the large circle, then r=x and the area of the larger circle is
A=x%5E2%2Api
and if x is the diameter of the small circle,then r=x%2F2 and the area of the smaller circle is
A=%28x%2F2%29%5E2%2Api->A=%28x%5E2%2F4%29%2Api

the ratio is:

%28x%5E2%2Api%29%2F%28%28x%5E2%2F4%29%2Api%29

=%28x%5E2%2Api%29%2F%28%28x%5E2%2Api%29%2F4%29

=4%28x%5E2%2Api%29%2F%28x%5E2%2Api%29

=4cross%28%28x%5E2%2Api%29%29%2Fcross%28%28x%5E2%2Api%29%29
=4