Finding the Volume of Prisms and Cylinders (or, “How a cheese slicer can help you learn about math!”)

Do You Like Memorizing? The old way to find the volume was to just memorize the formulae... Rectangular Prism Cylinder Triangular Prism Trapezoidal Prism l w h r h l w h d h

Memorizing is... Messed Up! It’s hard to remember the formulae. It’s easy to get them wrong this way. It’s one of the most common reasons people don’t like doing volume problems. And let’s face it - memorizing more formulae is no fun!

So Don’t Memorize - Slice Instead! Imagine that the object has been sliced into really, really, really thin slices - like you could do with a cheese slicer. For instance, a cylinder that looks like this would look like this sliced up, but with its slices stacked back together. Cool, huh!

First, Focus on Just One Slice Take an end slice and just focus on it to find its area. r r r The area of the end slice is easy: like always!

Then Multiply the Area by How Long the Cylinder Is Why? Watch as the slices get stacked together again... r r POOF! The cylinder is once again whole, its volume made up of all those slices. This shows why you have to multiply the area of the end slice by the length of all the slices to get the volume. Thus, V = area of the end slice times the length of the cylinder.

Connecting to the Formula r h So we multiply the area of the end slice (called a base) by the length of the cylinder. The length of the cylinder is usually called the height because... r h... When you stand it up on end like this, the length is how high it is. See! (But it doesn’t matter what you call it as long as you know what it is, and what to do with it.)

r h When you multiply the area of a base, By the height of the cylinder, h You get the formula for the volume of a cylinder: The important thing to remember is multiplying the area of a base times the length of the object!

It Works for Any Prism, Too! All prisms have at least one pair of congruent, parallel bases - just as cylinders do. Remember that bases are the “end slices.” Just remember to find the area of one base and multiply it by the distance to the other base! l Here, the formula would be:

Finally Can you figure out the formula for the volume of a trapezoidal prism, or at least tell me how to figure out the volume? What is the volume? Remember, the area of a trapezoid is: Click here to go to a site where you can practice some more on volume. Happy slicing, and good luck!here