Question

If the lengths of the radii of two circles are 1 and 4 respectively, what is the ratio of their circumference and of their areas?

Answer 1

Circumference of a circle based on its radius
`C_r = 2pir`
The circumference of a circle is in direct proportion to the radius.
So two circles with radii in the ratio `1:4` will have circumferences in the ratio `1:4`

Area of a circle based on its radius
`A_r = pir^2`
The area of a circle is in direct proportion to the square of its radius.
So two circles with radii in the ration `1:4` will have areas in the ratio `1:16`