How does the area of a circle change if the radius is multiplied by a factor of n, where n is a whole number?
THANK YOU!
First see my correction to your previous question of this type
http://www.jiskha.com/display.cgi?id=1452575743
if the ratios of the radii is in the ratio of 1 : n
then the ratio of their areas is 1 : n^2
that is,
if the radius is multiplied by a factor of n, where n is a whole number,
then the area is multiplied by a factor of n^2
What does ^ mean
^means exponents i think
^ does mean that the number following is an exponet
To understand how the area of a circle changes when the radius is multiplied by a factor of n, we need to know the formula for the area of a circle. The formula is given by A = πr^2, where A is the area and r is the radius.
If the radius is multiplied by a factor of n, the new radius becomes nr. Substituting this value into the formula, we get the new area of the circle: A' = π(nr)^2 = πn^2r^2.
From this equation, we can see that when the radius is multiplied by a factor of n, the area is multiplied by a factor of n^2. This means that the area increases quadratically as the radius increases.
For example, if the radius is doubled (n = 2), then the area will be quadrupled (n^2 = 4). If the radius is tripled (n = 3), then the area will be nine times larger (n^2 = 9), and so on.
So, to summarize, when the radius of a circle is multiplied by a whole number n, the area of the circle is multiplied by n^2.