To draw a scaled copy with a scale factor of 2 of a circle whose radio is r1, draw another circle with a radio r2=2r1, for example, if the radio of your first circle equals 2, the radio of your scaled circle is 2*2=4, like this:
The circumference of a circle is given by the formula:
[tex]C=2\pi r[/tex]Since the first circle has a radio r1, its circumference is:
[tex]C1=2\pi r1[/tex]And the second circle has a radio that is two times the radio of the first circle (2r1), its circumference is:
[tex]C2=2\pi(2r1)=2\times2\pi r1=4\pi r1[/tex]By taking the ratio of the circumference of circle two to the circumference of circle one, we get:
[tex]\frac{C2}{C1}=\frac{4\pi r1}{2\pi r1}=\frac{4}{2}\times\frac{\pi r1}{\pi r1}=\frac{4}{2}=2[/tex]Then, the circumference of the scaled circle is two times the circumference of the circle one.
The area of circle one is given by the formula:
[tex]A1=\pi(r1)^2[/tex]And the area of the scaled circle, whose radio is 2r1, is:
[tex]A2=\pi(2r1)^2=\pi2^2r1^2=4\pi r1^2[/tex]By taking the ratio of A2 to A1, we get:
[tex]\frac{A2}{A1}=\frac{4\pi r1^2}{\pi r1^2}=4\times\frac{\pi r1^2}{\pi r1^2}=4[/tex]Then, the area of the scaled copy is 4 times the area of the first circle