To figure out most circle questions, you need to be able to relate radius, diameter, circumference and area to each other easily.

Here’s a table summarizing how they are related:

Given this table, let’s try to solve this problem:

If the area of a circle, A, is expressed in terms of is diameter A = (πd2)/c then what is c?

Looking at the table relating diameter and area,  A = π(d/2)² = πd²/4

Comparing that to the given equation, you can see that c = 4.

Relating circumference to area takes a few more steps, but as long as you know how to find radius or diameter, you can work it out.

If the circumference, C of a circle is < 16π then what could be the area, A, of the circle?

If C < 16π, then 2πr < 16π where r is the radius of the circle

Dividing by 2π on both sides, this simplifies to r < 8

Since you know how to relate radius to area, this means that A = πr² < π8² = 64π

So the area A must be any value < 64π.

The question could also incorporate algebra and Pythagoras’ theorem to make finding the diameter or radius more complicated.

Let’s take a look at the question below.

In the circle above, if the area of the rectangle set inside the circle is 200 and b = 8a, what is the circumference of the circle?

You’re given the area of the rectangle and an equation relating the length and width.  This means that you can solve for a and b.

Area of a rectangle = ab = a(8a) = 200

Thus, a = 5.

Since b=8a, b=40.

You can now apply the Pythagoras Theorem to determine the diameter of the circle, which is given by

Thus, the circumference is 40.3π

Practice more questions like this one on Grockit!