If the radius of a circle is doubled, by what factor will the area change?

Thanks

According to the principle of proprotionality, it's by 4.

How? Well, you may insert into a certain radius, for example 2. Area will be pi (r^2), i.e. 4pi (we'll keep to pi to facilitate matters.).

Now, double the radius, i.e. 4. New area is pi(4^2) , i.e. 16pi.

You'll find out that the change in factor is squared the increase in radius (when you multiply that radius only though.)

Hope that helped!

WOW this is all another language to me. Thanks for your help

Hum, you know what is pi? \pi

Not really I'm trying to learn on my own by reading and so far not so good.

Well, this is an irrational number used in nearly all circular calculations including perimeter, area, volume of sphere, etc. You may come across it as \frac{22}{7} or 3.14.