How to Draw a Line as Volume

Lay out your graph by creating an x-axis and y-axis on an 8-by-10 inch sheet of graph paper. Allow the two axes to meet near the lower left-hand corner, but leave some room for a border between each axis and the border of the paper. Using a starting point that is indented for a distance of two squares makes for a very readable graph. Now, go ahead and create your two axes using a pencil and the straight edge.

Choose the square area of the base as your x-axis and then using the height of the cube as the value for the y-axis.

Choose a number with a whole integer as a square root. This makes finding the midpoint of the curve a little bit easier. Since it is possible to plot for than one curve on a graph, when using this method, three values will be chosen for the volume, 25, 64 and 100. Notice that the square roots are 5, 8 and 10, all whole numbers.

Establish a scale for the graph. Since we will be using whole numbers up to a 1,000, each line in the graph should equal between 5 and 10 on the numerical scale.

Find the midpoint of each curve. This point will be equal to the square root of each total volume, which in this example are 5, 8 and 10. What happens next is that you will plot three points. One will have an x and y value of 5, the next one will have 8 as both its x and y value. The last point will be located at 10 and 10. Although all three points fall on a straight line that forms a 45-degree angle from point zero, each point is part of a different curve.

Go ahead and calculate more points for the curved line that represents the volume of 100. Since V (volume) = x X y, and we know the value of V, all we have to do is assign a number to x and divide that number into 100. For example, if x = 5, then y = 20 and vice versa. If x = 50, then y = 2 and again the opposite is true. If x = 4, then y = 25 and if x = 1, then y = 100. This will give us enough data to plot a curve with one of the colored pencils and French curve.

Extend the path of the curve past 100 by using fractions expressed as decimals and larger numbers. For example, if x = 200, then y = 0.5 and if x = 500, y = 0.2. And, finally, if x = 1,000, then y = 0.1. Keep in find that in every case the value for x and y are reversible. Now you can complete one of the curves. Be sure to give the curve its own color and notice how the line approaches zero, but never actually becomes zero.

Complete the other two curves in the same manner, using a different color to express each one.