Question

Circle O is dilated by a scale factor r = 3. The image, circle O', has an area of 225m cm?.

What is the radius of circle O?

Answer 1

The radius of the circle O is R = 2.82 centimeters.

How to find the radius of circle O?

If we have a circle of radius R, and we dilate it by a scale factor k, the new radius is:

k*R

And we know that the area of a circle of radius R is:

A = pi*R²

Where pi = 3.14

If the radius of circle O is R, we know that O' is a dilation of scale factor 3, then the new radius is 3R

And we know tha tthe area of O' is:

A' = 225 cm² = 3.14*(3R)²

Now we can solve that to get the value of R.

3R= √( (225 cm²)/3.14)

3R = 8.46 cm

R = 8.46cm/3

R = 2.82cm