Answer:
The circumference will be [tex]4[/tex] times greater than the original
Step-by-step explanation:
we know that
The circumference of a circle is equal to
[tex]C=2\pi r[/tex]
where
r is the radius of the circle
In this problem we have
The radius of the original circle is
[tex]r1=16\ cm[/tex]
The circumference of the original circle is equal to
[tex]C1=2\pi (16)=32\pi\ cm[/tex]
If the circumference is dilated by a scale factor of [tex]4[/tex]
then
the radius of the dilated circle will be
[tex]r2=4*16=64\ cm[/tex]
and the circumference of the dilated circle will be
[tex]C2=2\pi (64)=128\pi\ cm[/tex]
so
[tex]C2=4C1[/tex]
therefore
The circumference will be [tex]4[/tex] times greater than the original
