Volume of a Cylinder

Review: In past lessons, we learned the formula for the volume of a rectangular prism. Now we will use that knowledge to create a new formula.

The BASE of the rectangular prism is highlighted in GREEN.

What shape is the BASE of the Rectangular Prism?

What is the area of the BASE of the rectangular prism above?

Attempt to re-write the formula for the volume of the rectangular prism using BASE.

NOTICE

Notice that BASE demonstrates a two-dimensional figure. When we refer to BASE (capitalized) in class, we are referring to a two-dimensional figure. I.e. something you can take the area of.

Now, here is a CYLINDER with a radius of 3 units and a height of 10 units. Feel free to rotate it and observe.

The cylinder's BASE is highlighted in pink.

[br]a. What is the shape of the cylinder's BASE?[br]b. What is the general formula for the area of this particular BASE?

What is the area of the BASE of this cylinder given the radius is 3 units? You may leave "pi" in your answer.

Discovery

Using your knowledge of your NEW formula for the volume of a rectangular prism (V=BASE*height) and the area formula for the BASE of a cylinder, can you find the formula for the volume of a cylinder?

Using your equation for the volume of a cylinder, what is the volume of the cylinder above given the radius is 3 units and the height is 10 units? You may leave "pi" in your answer.