Question

Modeled Problems Instructions

Goal:

Demonstrate a deep understanding of how to calculate the volume of a variety of prisms and cylinders.

Finished Product:

Detailed calculations with justification for finding the volume of the following figures:

Cylinder

Triangular Prism (Any, not necessarily an equilateral triangle)

Rectangular Prism

Trapezoidal Prism

Prism with any regular polygon as its base (Don't you dare copy mine and use a pentagon!)

 

Example:

Prism with Regular Pentagon Bases

We find the volume of a prism by calculating the area of the base and multiplying that by the height of the prism. If a prism has two regular pentagons as its base, we need to calculate the area of each pentagon and then multiply that area by the perpendicular distance between the bases, or the height of the prism.

To find the area of a regular pentagon, we use the area formula for a regular polygon:

Area of Regular Polygon = (\frac{1}{2})(apothem)(side length)(r

Then we would multiply that area by the height of the prism to find that:

Volume of Prism with Regular Pentagon Bases = (\frac{1}{2})(ar

 

To find the volume of this pentagonal prism, we would substitute the appropriate values into the above formula.