Question

If the circumference of a circle is doubled, how does the area of the circle change?
A) The area is doubled.
B) The area is tripled.
C) The area is quadrupled.
D) The area does not change.

Answer 1

The area is doubled

Answer 2

Circumference

\[C= 2\pi r\]

Area

\[A = \pi r ^2\]

Answer 3

C=2πr
A =πr^2
So
A=Cr/2
If it is doubled
A=Cr
A=2πr^2

Answer 4

Are you sure the area only doubled when you double the radius???

Answer 5

Maybe the radius didn't double, but if the circumference double, then the diameter had to double, so how much has the radius changed?

Answer 6

So D^2 becomes 4 D^2

Answer 7

Conclude

Answer 8

area is increased by a factor of 2^2

Answer 9

Lets examine a hpothetical circle that has a circumference of 4 pi inches. That would mean for this circle the radius was 2 in. Thus the Area would be 4 pi square inches (remember that)
Now we double the circumference giving us 8 pi inches and a radius of 4 inches. The area A which is pi r^2 would now be 16 Pi square inches, compare the Areas, it appears to me that the area has quadrupled!

Answer 10

welshfella just re-enforced what I was thinking.

Answer 11

if you scale the linear dimension by x , the area will scale by x^2 and the volume by x^3
this works for all "normal" figures/shapes