Circles (Circumference and Area)
Figure 1
This page looks applying the formulas to work out the circumference and area of a circle.
The circumference of a circle is the length of the circle.
Lets say the circumference of the circle is represented by the letter C.
Then C = 2πr, the r = radius of the circle.
When working out the area of a circle, we use the formula,
A = πr2, where A = area of a circle
The two components of a circle which we use to work out both area and circumference are the diameter and radius.
The radius (in blue in figure 1) is the LENGTH of a line that goes from the centre of the circle to a point on the circle.
The diameter (in orange in figure 1) is the length of a line that goes from one point to another point on the circle, however that line also goes through the centre of the circle.
As a result, the diameter is the always twice the radius and as shown in the diagram.
The circumference of a circle is the length of the circle.
Lets say the circumference of the circle is represented by the letter C.
Then C = 2πr, the r = radius of the circle.
When working out the area of a circle, we use the formula,
A = πr2, where A = area of a circle
The two components of a circle which we use to work out both area and circumference are the diameter and radius.
The radius (in blue in figure 1) is the LENGTH of a line that goes from the centre of the circle to a point on the circle.
The diameter (in orange in figure 1) is the length of a line that goes from one point to another point on the circle, however that line also goes through the centre of the circle.
As a result, the diameter is the always twice the radius and as shown in the diagram.
Video 1
Video 1
Video 2
Video 2
Video 1 (Explanation)
Video 1 (Explanation)
Question: Find the circumference of a circle with diameter 10cm.
Using the formula C = 2πr = 2 x π x r, where C is the circumference, we can substitute r with 5.
This gives us
C = 2π x 5 = 10π
How did we get the radius?
Well, the question tells us the diameter, and we know that the diameter is equal to twice the length ofthe radius.
Thus if the diameter is 10cm, then the radius = 10cm/2 = 5cm.
Another way of writing the formula of the circumference is
C = π x d, where d = diameter
Why?
Well the diameter is equal to twice the radius, so we can write that d = 2r = 2 x r
So
2πr = 2 x π x r = 2 x r x π = d x π
Video 2 (Explanation)
Video 2 (Explanation)
Question: If the radius of a circle is equal to 3cm, work out the area of that circle.
Using the formula A = πr2, where A is the area of the circle, we can substitute r with 3, and thus work out the area, as shown below.
A = π x 32 = 9π
Another way of writing the formula for the area of a circle is
A = π(d/2)2 = π x (d/2)2
Why?
Well if we remember that diameter is equal to twice the radius, we can write d = 2r.
So if we want to find out what the radius equals, we can rearrange the formula to make r (radius) the subject as shown below.
d = 2r
(Divide by 2)
d/2 = 2r/2
d/2 = r
So we can substitute r with d/2 in A = π x r2 to get A = π x (d/2)2
MAKE SURE THAT WHEN WORKING OUT THE AREA AND CIRCUMFERENCE OF A CIRCLE YOU UNDERSTAND THERE ARE DIFFERENT WAYS OF WRITING THE FORMULAS., AS EXPLAINED ABOVE.