Finding the circumference and area of circles can be confusing because their formulas are so similar. Additionally, sometimes you aren’t given exactly what you need to solve the problem, and you have to perform a calculation before solving for circumference and area.

Have no fear! In the example problems below we’ll help you understand how to solve for the circumference and area of circles.

EXAMPLE 1: Find the circumference and area of the given circle:

CIRCUMFERENCE:

The formula for the circumference of a circle is C = 2πr, where r is the radius.
In the circle, the radius is 3 ft, so we’ll substitute 3 ft for r in the equation.
C = 2πr
C = 2π(3 ft)
C = 6π ft
C ≈ 18.8 ft

AREA:

The formula for the area of a circle is A = πr², where r is again the radius.
In the circle, the radius is 3 ft, so we’ll substitute 3 ft for r in the equation.
A = πr²
A = π(3 ft)²
A = π(3 ft)(3 ft)
A = π(9 ft²) or 9π ft²
A ≈ 28.3 ft²

EXAMPLE 2: Find the circumference and area of the given circle:

Now, this circle poses a problem. We need to know the radius (the distance from the center of the circle to the edge of the circle) for our circumference and area formulas, but in the image above, we’re given the diameter (the distance across the entire circle).

All we have to do is a simple calculation, and we’ll have our radius.
The radius of a circle is half the diameter.
r = ½d
r = 1/2 (10 meters)
r = 5 meters

Now we’re reading to calculate the circumference and area!

CIRCUMFERENCE:

The formula for the circumference of a circle is C = 2πr, where r is the radius.
In the circle, the radius is 5 meters, so we’ll substitute 5 meters for r in the equation.
C = 2πr
C = 2π(5 meters)
C = 10π meters
C ≈ 31.4 meters

AREA:

The formula for the area of a circle is A = πr², where r is again the radius.
In the circle, the radius is 5 meters, so we’ll substitute 5 meters for r in the equation.
A = πr²
A = π(5 meters)²
A = π(5 meters)(5 meters)
A = π(25 meters²) or 25π meters²
A ≈ 78.5 meters²