Learn about Circumference and Area of a Circle In this lesson, let’s learn about circumference and areas of circles. We are to find the circumference and area of a circle where we are given the diameter is 16 centimeters and we’re asked to use Pi as 3.14. So, let me first draw a circle and let’s mark the basics. So if this is the center of the circle, this length is called the radius and the diameter is a line that touches two end points and passes through the circle. So, this is called the diameter. The radius of the circle is always ½ of the diameter which makes sense. It goes from one end point to the center but doesn’t go all the way to the other end point. Now, the formula to remember is the perimeter of the circle is two times Pi which is a value that we usually uses 3.1422 over 7 multiplied by the radius or two times the radius is diameter anyway so I can also have this be Pi times the diameter. That’s the perimeter. Area of a circle is Pi times the radius squared. Now, the value of Pi is usually 22/7. Pi can also be 22/7 or I can approximate this as 3.14. So, let’s try and attack this problem. We are given the diameter equals 16 centimeters so the radius is half that or 16 over two centimeters or 8 centimeters. So if we have to compute the perimeter, I can use two times Pi times the radius R or radius R. Let’s use upper case or like we did here, two times Pi times R which is two times 3.14 multiplied by R which is 8 centimeters. So this is 16 times 3.14 which is 50, 16 times 3.14 is 50.24 centimeters. So, the perimeter of this circle is 50.24 centimeters and the way I got that is by just using this formula. Now, when we want to compute the area, that’s Pi times R squared which is 3.14 times what’s R? 8 squared or 3.14 times 64 centimeters squared because 8 centimeters times 8 centimeters is 64 centimeters squared. This is 200.96 centimeters squared. So, the area, this is the formula is 200.96 centimeter squared. Key things to remember that we’ve covered in this lesson, remember the radius is always half the diameter. Perimeter is two times Pi times the radius or Pi times the diameter because two times radius is equal to the diameter anyway and area is Pi times R squared where R is the radius.