Circle geometry
Watch this video to learn about circle geometry.
Arc length
The circumference of a circle = \(\pi d\) or \(2\pi r\).
Look at the sector of the circle shown below. To calculate the length of the arc, we need to know what fraction of the circle is shown. To do this, we use the angle and compare it with 360藲.
This angle is 144掳.
That is \(\frac{{144^\circ }}{{360^\circ }} = \frac{2}{5}\) of a full turn (360掳).
So the arc is \(\frac{2}{5}\) of the circumference.
\(c=\pi d=3.14\times 6\) (Remember the diameter is double the radius.)
\(=18.84cm\)
Arc length = \(\frac{2}{5}\times 18.84 = 7.54cm\)
(There is so need to simplify \(\frac{144}{360}\), you can use this in the arc calculation instead of \(\frac{2}{5}\).)
The formula used to calculate the Arc Length is:
\(Arc\,length = \frac{{Angle}}{{360^\circ }} \times \pi d\)
Now try the example question below.
Question
Calculate the length of the arc shown in the diagram below.
\(Arc\,length = \frac{{Angle}}{{360^\circ }} \times \pi d\)
Remember also that \(d = 2 \times r\)
\(= \frac{{150}}{{360}} \times \pi \times (2 \times 4)\)
\(= \frac{{150}}{{360}} \times \pi \times 8\)
\(= 10.47cm\)
More guides on this topic
- Determine the gradient of a straight line
- Calculating the volume of a standard solid
- Applying Pythagoras Theorem
- Applying the properties of shapes to determine an angle
- Using similarity
- Working with two-dimensional vectors
- Working with three-dimensional coordinates
- Using vector components
- Calculating the magnitude of a vector
- An Approximate History of Co-ordinates