11.3.7 Drawing a Graph

The following data values were collected on the circumferences and diameters of various circular objects. All of the measurements are in inches.

Diameter (in.) Circumference (in.)
4.4 14.1
6.6 20.9
8.6 27
10.3 32.3
23.0 72.8

Solution symbolActivity: Drawing a Graph

(a) On some graph paper or in your notebook, plot these points on a graph with the diameter on the horizontal (x) axis and the circumference on the vertical (y) axis. Draw a straight line through the points.

Hint symbol

Comment

Remember to refer back to the summary of how to draw a graph so that you include all the detail needed. In particular look at the data you are given carefully before you decide what scale to use for the x- and y-axes.

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Answer

(a) Your graph should look like this:

Note the title and labeling of the axes.  You may have used a different scale from us if you had different graph paper. This is fine as long as it makes best use of the paper and is easy to read from.

(b) Use your graph from part (a) to estimate the circumference of a circle of diameter 15 inches.

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Answer

(b) To find the circumference of a circle of diameter 15 inches, find 15 on the horizontal axis. From this point, draw a vertical line to meet the graph. Then draw a horizontal line across to the vertical axis and read off the value. The circumference of a circle of diameter 15 in. is about 47 inches.

(c) Use your graph from part (a) to estimate the radius of a circle of circumference 30 inches.

Hint symbol

Comment

Remind yourself about what is the radius of a circle—you may have it in your math notebook.

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Answer

(b) The circumference is 30 in., so find 30 on the vertical axis. From this point, draw a line horizontally across to the graph, then vertically down to the horizontal axis. The point where this line crosses the horizontal axis gives the diameter of a circle whose circumference is 30 inches. It is about 9.5 inches, so the radius of the circle will be half of this, about 4.7 to 4.8 inches.

Optional Brain Stretcher

This is an interesting graph as you can make an estimate for π (pi) from it. π is the ratio of the circumference to the diameter of any circle and is a constant.

By measuring the slope (gradient) of the graph that you have drawn you will obtain an estimate for π.  This is calculated by dividing the rise of the line by corresponding run of the line as shown below.

Have a go and see if you get a value close to 3.141.

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Answer

Gradient = rise = 72.8 in – 14.1 in = 58.7 in = 3.156 (to 3 d.p.)

                run     23.0 in – 4.4 in      18.6 in

This is not a bad estimate for pi!

For more practice in drawing and interpreting graphs, try:

In the next section we will look at bar charts and the different ways that these can be drawn depending on the data that you have and what you want to show.

11.3.6 Using the Graph

11.4 Bar Charts