Question

In the diagram above, if the circle with center F has an area of

72 , what is the area of the circle with center G?

Answer 1

Here is a diagram.

Answer 2

ooh - let me look at that agin....

Answer 3

And here are the answer choices if you need them.
18
24
30
36
48

Answer 4

area of large circle = pi * r^2 where r is radius
radius of small circle = r/2 so
area of small circle = pi * (r^2/4)
ratio of areas = pi r^2
------- = 4:1
pi r^2/4

so area of small circle = 72/4 = 18

Answer 5

Thank you.

Answer 6

a simpler way to do it is to use the fact that similar shapes have areas whose ratio is the square of corresponding dimensions

eg if you have a square 2 * 2 and another 4 * 4

then ratio of their areas = 2^2 : 4^2

Answer 7

in this case the radii are 1: 2 so areas are 1: 4

1 /4 = x / 72

x = 18

Answer 8

That is simpler than your first response. Thanks again.