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?

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Answer 1 · 2015-12-30T11:48:41

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

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

A circle has a radius of 99 inches. The radius is multiplied by 2/32/3 to form a second circle. How is the ratio of the areas related to the ratio of the radii?