SAT Subject Test Mathematics Level 2

CIRCLES—FOUR FORMULAS

After the triangle, the test makers’ favorite plane geometry figure is the circle. Circles don’t come in
as many varieties as triangles do. In fact, all circles are similar—they’re all the same shape. The only
difference among them is size. So you don’t have to learn to recognize types or remember names.
All you have to know about circles is how to find four things:

You could think of the task as one of memorizing four formulas, but you’ll be better off in the end if
you have some idea of where the arc and sector formulas come from and how they are related to
the circumference and area formulas.

Circumference: Circumference is a measurement of length. You could think of it as the perimeter:
It’s the total distance around the circle. If the radius of the circle is r,

Circumference   =   2πr

Since the diameter is twice the radius, you can easily express the formula in terms of the diameter d:

Circumference   =   πd

In the circle above, the radius is 3, so the circumference is 2 π(3) = 6π.

Circumference

Length  of  an  arc

Area

Area    of  a   sector