The radius is an important part of figuring out both the area and the circumference of a circle. Knowing the radius helps us understand what makes up a circle.

1. Circumference: The circumference is the distance around the circle. We can find it using this formula:

   $C = 2\pi r$

   In this formula, $r$ is the radius. This means that as the radius gets bigger, the circumference gets bigger too.

   For example, if the radius of a circle is 3 units, we can calculate the circumference like this:

   $C = 2\pi(3) = 6\pi$

   So, the circumference will be $6\pi$ units.

2. Area: The area is the space inside the circle. We can find the area with this formula:

   $A = \pi r^2$

   In this case, the area increases based on the square of the radius.

   For instance, if the radius is 4 units, we can find the area like this:

   $A = \pi(4^2) = 16\pi$

   So, the area will be $16\pi$ square units.

Understanding the radius is key! It helps us not only figure out how big circles are but also how they relate to each other.