SOLUTION: If a small circle's diameter is a large circle's radius, then the small circle is ____% of the large circle's area? a) 20 b) 25 c) 30 d) 40 e) 50

Algebra ->  Circles -> SOLUTION: If a small circle's diameter is a large circle's radius, then the small circle is ____% of the large circle's area? a) 20 b) 25 c) 30 d) 40 e) 50      Log On


   



Question 288049: If a small circle's diameter is a large circle's radius, then the small
circle is ____% of the large circle's area?
a) 20 b) 25 c) 30 d) 40 e) 50

Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!



The green line is the small circle's diameter and also the 
large circle's radius.  Suppose the green line is 2 inches long.
Then the small circle's radius is 1, the red line:



Area of small circle = pi%2Aradius%5E2=pi%2A1%5E2=pi%2A1=pi

Area of large circle = pi%2Aradius%5E2=pi%2A2%5E2=pi%2A4=4pi

Since the big circle's area is 4 times the small circle's area,
the small circle's area is 1%2F4 of the big circle's area
and 1%2F4 is the same as 25%. So the correct choice is b)

Edwin