Question

If the length of the radius of the circle is doubled, how does that affect the circumference and area. Explain please.

Answer 1

radius - r
area:

`A_1=\pi r^2`
circumference:

`C_1=2 \pi r`

the length of the radius is doubled
radius - 2r
area:

`A_2=\pi * (2r)^2=\pi * 4r^2=4 \pi r^2`
circumference:

`C_2=2 \pi * 2r=4 \pi r`


`(A_2)/(A_1)=(4 \pi r^2)/(\pi r^2)=4 \\ \\ (C_2)/(C_1)=(4 \pi r)/(2 \pi r)=(4)/(2)=2`

When the length of the radius is doubled, the area is quadrupled and the circumference is doubled.