Question

Given that the diameter of Circle A is 6 cm , and the radius of Circle B is 18 cm , what can be concluded about the two circles?

Answer 1

The radius of circle B is 6 times greater than the radius of circle A

The area of circle B is 36 times greater than the area of circle A

Explanation:

we have

Circle A

`D=6\ cm`

The radius of circle A is

`r=6/2=3\ cm` -----> the radius is half the diameter

Circle B

`r=18\ cm`

Compare the radius of both circles

`3\ cm< 18\ cm`

`18=6(3)`

The radius of circle B is six times greater than the radius of circle A

Remember that , if two figures are similar, then the ratio of its areas is equal to the scale factor squared

All circles are similar

In this problem the scale factor is 6

so

`6^(2)=36`

therefore

The area of circle B is 36 times greater than the area of circle A