- What is the smallest volume that you can create with this prism? _______________
What is the surface area associated with this volume? _______________
What is the depth? _______________
What is the height? _______________
What is the width? _______________
- What is the largest volume that you can create with this prism? _______________
What is the surface area associated with this volume? _______________
What is the depth? _______________
What is the height? _______________
What is the width? _______________
- Explain why the surface area is larger than the volume in #1.
- Can you make the surface area and volume have the same value? If so, what are the dimensions of the prism at that time? How close can you get?
Are the two values really the same (or close to the same) with
these dimensions? Hint: What are the units for each of the values? Are
the units the same?
- Change the rectangular prism so
that it is as large as possible in every direction.
In #2, you found that the largest possible volume of the rectangular prism
was _____________.
How do you think the largest possible volume of the triangular
prism will compare? Will it be larger or smaller?
How much larger or smaller?
Write your guess and reasoning here and then choose the triangular
prism to check it:
- Was your prediction correct?
Does the same ratio always hold true
for triangular and rectangular prisms with the same dimensions?
- Do the values for the surface area of the triangular and rectangular
prisms have the same ratio that you discovered in #5?
Why do you think this is true?
- Let's take a look at how we would calculate the surface area of the
triangular prism. Please set all dimensions at 14 units for this
exercise:
- Click on View Front. This view looks like a triangle. The base is 14
units and the height is 14 units.
Since the formula for the area of a triangle is:
the area of this face of the triangular prism is ________________.
Please show your work:
- Click on View Side. This view looks like a rectangle that is slanted
into the screen. The base is 14, but what is the height?
Can you use the Pythagorean theorem to find the height of this rectangle?
Hint: The height of this rectangle is the hypotenuse of a triangle in
another view!
Show your work:
What is the area of this side of the triangular
prism? Show your work:
- Click on View Top. This view looks like a regular rectangle. The area of
this face of the prism is _____________________. Please show your work:
- Now, since we have ____ faces that look like View Front, ___ faces that
look like View Side, and ___ faces that look like View Top, we can add the area
of the 5 faces to get the total surface area. What is it? Show your work:
