Question

A circle has a radius of `9` inches. The 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

The ration of the areas is the square of the ration of the radii.

Explanation:

`r_1 = 9`
`r_2 = 9*2/3 = 6`
`r_1/r_2 = 9/6 = 3/2`
The area of a circle is `pi*r^2`
`=> a_1/a_2 = (pi*9^2)/(pi*6^2) =(9/6)^2 = (3/2)^2 = 9/4`