Question

How will the circumference of the circle change if it is dilated by a scale factor of 4?

The circumference will be 4 times greater than the original.
The circumference will be 16 times greater than the original.
The circumference will be 1/4 the original.
The circumference will be1/16 the original.

Answer 1

since the diameter and the circumference have a linear relationship, the circumference will be 4x the original.

Answer 2

The circumference will be
`4` times greater than the original

Explanation:

we know that

The circumference of a circle is equal to

`C=2\pi r`

where

r is the radius of the circle

In this problem we have

The radius of the original circle is

`r1=16\ cm`

The circumference of the original circle is equal to

`C1=2\pi (16)=32\pi\ cm`

If the circumference is dilated by a scale factor of
`4`

then

the radius of the dilated circle will be

`r2=4*16=64\ cm`

and the circumference of the dilated circle will be

`C2=2\pi (64)=128\pi\ cm`

so

`C2=4C1`

therefore

The circumference will be
`4` times greater than the original