Answer:
[tex]\frac{16}{25}[/tex]
Step-by-step explanation:
Let's call the circles A (radius 4) and B (radius 5). With the area of a circle defined as πr² (where r denotes the radius),
[tex]Area_A = \Pi * 4^{2} = 16\Pi[/tex]
[tex]Area_B = \Pi * 5^{2} = 25\Pi[/tex]
When calculating the ratio between the areas we simply divide [tex]Area_A[/tex] by [tex]Area_B[/tex], the π's of both terms will cancel out.
[tex]\frac{Area_A}{Area_B} = \frac{16\Pi}{25\Pi} = \frac{16}{25}[/tex]
As a general rule, the ratio will always be [tex]\frac{(r_A)^{2} }{(r_B)^{2}} = (\frac{r_A }{r_B})^{2}[/tex]
