Question

Circle A has radius 4 feet .Circle B has
radius 9 feet .What is the ratio of the area of arcle A to the
area of circle B?

a . 1/2
b . 4/9
c . 8/27
d . 16/81​

Answer 1

Answer:

d. 16/81

Step-by-step explanation:

The formula of an area of a circle:

$A=\pi r^2$

r - radius

The ratio of the areas of the difference circles:

$\dfrac{A_1}{A_2}=\dfrac{\pi r_1^2}{\pi r_2^2}=\dfrac{r_1^2}{r_2^2}=\left(\dfrac{r_1}{r_2}\right)^2$

We have

Circle A: r₁ = 4ft

Circle B: r₂ = 9 ft

Substitute:

$\dfrac{A_A}{A_B}=\left(\dfrac{4}{9}\right)^2=\dfrac{16}{81}$