Question

Suppose a circle has a radius of 4.5 inches. If you double the radius of the circle, does the area of the circle double as well? What happens to the circle’s circumference? Explain and justify your reasoning.

Answer 1

C = 2pi * r
A = pi * r^2

double rand you get

C' = 2pi * (2r)
A' = pi * (2r)^2

Note that C' = 2C but A' = 2^2 A

if you multiply the size of dimensions by n,

perimeter is multiplied by n
area is multiplied by n^2
volume is multiplied by n^3