The circumference of a spherical pincushion is 2π cm. Find the surface area of the pincushion. Express your answer in terms of π.

The equation for circumference is C=pi*d (d=diameter)

So then we can plug in what we know:

2=pi*d

So then the diameter is equal to 2/pi (radius=1/pi)

Now the equation of surface area for a sphere is SA=4*pi*r^2

So we can plug in what we know:

SA=4*pi * (1/pi) (1/pi)

Some of the pi's cancel out so you are left with

SA=4/pi

4π because the radius is 1 and surface area is 4πr^2