Having formulas in measurement is very valuable as they can save us a lot of time. Before we beign, it will be helpful to recall the formula for area of a circle.

Use the applet below to complete the following procedure. Record values in the downloadable asset chart.

Procedure

The base of a cylinder is a circle. Pick a radius you want to work with by moving the slider, but leave the height at 1 unit.
Calculate the area of the circular base to one decimal place. Record this value.
Reveal the volume of the cylinder and record this value.
Change the radius to a different value and compute the area of the base and the volume of the disk with a height of 1 unit once again. Record these values.
Slide the height slider to the value of the height you would like to work with. Leave the radius where it is.
Reveal the volume of the cylinder with these measurements and record the values.

Use the following applet:

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Investigate

Consider the following questions once you have completed the above procedure.

How does the area of the circular base compare with the volume of a single disk (a cylinder of height 1 unit)? Explain why you think the area of the base and the volume of a single disk are related in this way.

How do you think the total volume of the cylinder is related to the volume of all of the single disks?

If you know the area of the base, how can you determine the volume of a cylinder? Does your answer change if the height is not a whole number?

Answer the questions below after you have completed the activity.

Discussion

Using r for radius and h for height, write a formula for the volume of a cylinder,V.

Outcomes

8.G.C.9

Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

Investigation: Formula for volume of a cylinder

Discover the formula for volume of a cylinder

Outcomes

8.G.C.9

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