Formula for the Circumference and Area of a Circle
Area and Circumference of a Circle
Area of a circle is found by multiplying Pi times the radius squared. The radius of a circle is a segment that has its end points on the circle, and on the center of the circle, or you can think of it like, it goes halfway across the circle.
Circumference, which is the distance around the circle, is 2 times Pi, times the radius, or Pi times the diameter. The diameter of a circle is a segment that passes through the center of the circle and has its end points on the circle, or it goes all the way across your circle.
The diameter is twice the radius. Likewise, the radius is half of the diameter. These formulas are interchangeable since when you multiply 2 times the radius you get diameter. Let’s look at an example. Find the area and circumference of the following circle in terms of Pi and to the nearest tenth.
In our example all they’ve given us is the diameter, but that’s all we need to find our area and to find our circumference. We’ll start with area. The first thing we’re going to do is write our formula for area. Area is Pi times radius squared.
Now we need to substitute our radius, but they only gave us the diameter. Keep in mind that the radius goes half way across your shape, or that it’s half the diameter. Your radius is half of your diameter, so the radius is half of 22 centimeters, which means that the radius is 11 centimeters.
Now we’ll substitute 11 centimeters for our radius, so our area is Pi times 11 centimeters squared. We need to follow PEMDAS, so we need to square our radius first (take care of our exponents first). 11 squared is 121, centimeters squared is centimeters squared, 121 centimeters squared times Pi is 121 Pi centimeters squared.
They asked us to find our area and circumference in 2 different ways. The first way was in terms of Pi. This answer is the area of our circle in terms of Pi, which means leave Pi in your answer, or don’t multiply times Pi. This would be 1 of our answers.
The second way they asked us to find area was rounded to the nearest 10, so now we do need to multiply times Pi, and when you multiply 121 times Pi you get that the area is about 380.1327, etc. Since they asked us to round the tenths place, the 1 is in the tenths place, but the 3 tells the 1 what to do.
The 3 tells the 1 to stay the same, so that would be 380 and 1 tenth centimeters squared. Circumference we can use either one of these formulas to find. Since we were given the diameter, we can just use our circumference equals Pi times diameter formula.
Now we need to substitute our diameter, the circumference is Pi times 22 centimeters, which is 22 Pi centimeters, and that gives us the first answer they asked for in terms of Pi, 22 Pi centimeters.
To find the answer to the nearest tenth, we now need to multiply 22 times Pi, so that we get circumference is 69.1150, etc., and then we round to the tenths place, the 1 is in the tenths place, and the 1 next to it tells it to stay the same, so our circumference is 69 and 1 tenth centimeters.