Question

A circle has a radius of 9 inches. The is radius is multiplied by `2/3` to form a second circle. How is the ratio of the areas related to the ratio of the radii?

Answer 1

Please refr to the Explanation.

Explanation:

Let, `A_i and r_i,` denote the Area and Radius of `i^(th)`

circle where, `i=1,2.`

Clearly, `A_i=pir_i^2.`

`:. A_1/A_2=(pir_1^2)/(pir_2^2)=r_1^2/r_2^2=(r_1/r_2)^2....(star).`

Given that, `r_2=2/3*r_1, or, r_1/r_2=3/2,` we have, from `(star),`

`A_1/A_2=(3/2)^2=9/4=2.25`