Question

How does doubling the radius of a circle affect its area?

Answer 1

`"area increases by a factor of 4"`

Explanation:

`"the area of a circle is "`

`A=pir^2larrcolor(blue)"original area"`

`"doubling the radius that is "r=2r`

`rArrA=pi(2r)^2=4pir^2larrcolor(blue)"area after doubling"`

`"the area has increased by a factor of 4"`

Answer 2

See below.

Explanation:

When you enlarge a linear measurement by a scale factor `a` the area changes by a scale factor `a^2`

So when you double the radius. scale factor 2, the area is increased by a scale factor:

`2^2=4`

So the area is quadrupled in this case.