Question

32. Draw a scaled copy of the circle using a scale factor of 2b. How does the circumference of the scaled copy compare to the circumferenceof the original circle?How does the area of the scaled copy compare to the area of the original circle?

Answer 1

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:

`C=2\pi r`

Since the first circle has a radio r1, its circumference is:

`C1=2\pi r1`

And the second circle has a radio that is two times the radio of the first circle (2r1), its circumference is:

`C2=2\pi(2r1)=2*2\pi r1=4\pi r1`

By taking the ratio of the circumference of circle two to the circumference of circle one, we get:

`(C2)/(C1)=(4\pi r1)/(2\pi r1)=(4)/(2)*(\pi r1)/(\pi r1)=(4)/(2)=2`

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:

`A1=\pi(r1)^2`

And the area of the scaled circle, whose radio is 2r1, is:

`A2=\pi(2r1)^2=\pi2^2r1^2=4\pi r1^2`

By taking the ratio of A2 to A1, we get:

`(A2)/(A1)=(4\pi r1^2)/(\pi r1^2)=4*(\pi r1^2)/(\pi r1^2)=4`

Then, the area of the scaled copy is 4 times the area of the first circle