FSR - Circles and Pie Charts Lesson

Circles and Pie Charts

Introduction

Pie charts can be used to display different category percentages. The percentages are the category's proportion of the whole. It's important that a pie chart is displayed using the correct portion of the circle for each category. Otherwise, the pie chart may come off as misleading. There are two tools that can be used when working with circles.

A compass can be used to draw a circle.

A protractor can be used to measure the angles of a circle.

Let's take a look at how we can use these tools to construct a pie chart.

Sectors and Central Angles

Categories in a pie chart are segmented out by sectors. Sectors in a circle are the pizza slice-shaped part of the circle. In the chart below, you can see that we have 5 sectors.

Each sector has a central angle that is associated with the size of the sector. A central angle in a circle is the angle at the center of the sector. The central angle of all sectors will always add to 360 degrees. If we know the percentage of a category in a pie chart, then we can find the central angle of the sector. Since percentages add to 100 and angles add to 360, we'll use the following formula.

Central angle for a category = $\frac{Value of the component}{Sum of the values of all components}$ × 360°

Example: Jaclynn has a monthly salary of $3,700. She is trying to form a budget and wants to create a pie chart for her expenses.

Food	Shopping	Rent	Savings	Miscellaneous
800	500	2000	250	150

Calculate the central angles for each category.

The total amount earned by Jaclynn is $3,700. We'll use this value as the denominator.

Item	Amount (in $)	Central Angle
Food	800	$LaTeX: \frac{800}{3700}\cdot360=78^{\circ}$ $\frac{800}{3700}\cdot360=78^{\circ}$
Shopping	500	$LaTeX: \frac{500}{3700}\cdot360=49^{\circ}$ $\frac{500}{3700}\cdot360=49^{\circ}$
Rent	2000	$LaTeX: \frac{2000}{3700}\cdot360=194^{\circ}$ $\frac{2000}{3700}\cdot360=194^{\circ}$
Savings	250	$LaTeX: \frac{250}{3700}\cdot360=24^{\circ}$ $\frac{250}{3700}\cdot360=24^{\circ}$
Miscellaneous	150	$LaTeX: \frac{150}{3700}\cdot360=15^{\circ}$ $\frac{150}{3700}\cdot360=15^{\circ}$

Great! Now, that we have the central angles. We can use the compass and the protractor to draw the pie chart.

Finding Percentage from the Central Angle

We can also find the percentage of a sector in a pie chart when given the central angle.

$LaTeX: \frac{CentralAngle}{360}=\frac{Percentage}{100}$ $\frac{CentralAngle}{360}=\frac{Percentage}{100}$

Example 1: The central angle of a sector is 72^o. What percentage of the circle is comprised of the sector?

$LaTeX: \frac{72}{360}=\frac{x}{100}$ $\frac{72}{360}=\frac{x}{100}$

LaTeX: 7200=360x $7200=360x$

LaTeX: 20=x $20=x$

Therefore, 20% of the circle is comprised of the sector.

Example 2: Try this one on your own and then check your answer below. A sector of a circle has a central angle of 135^o. What percentage of the circle does the sector occupy?

$LaTeX: \frac{135}{360}=\frac{x}{100}$ $\frac{135}{360}=\frac{x}{100}$

LaTeX: 13500=360x $13500=360x$

LaTeX: 37.5=x $37.5=x$

Therefore, 37.5% of the circle is comprised of the sector.

Circles and Pie Charts Practice

1. The following data is provided on the method of transport for students at a local high school. Calculate the central angles for each category. Then, draw and measure an accurate pie chart.

Bus	Bike	Train	Car	Skateboard
120	180	240	80	100

2. A sector of a circle has a central angle of 36^o. What percentage of the circle does the sector occupy?

3. A survey was given to 300 high schoolers asking them where they eat breakfast. The sector representing the students that eat at home is 100 degrees and the sector representing the students that eat at school is 175 degrees. What percent of students don't eat breakfast?

TO VIEW THE SOLUTIONS ONCE YOU HAVE PRACTICED, CLICK HERE. Links to an external site.

IMAGES CREATED BY GAVS