Filling and Wrapping: Three-Dimensional Measurement Name: ______________________ Per: _____
Investigation 2: Polygonal Prisms
Learning Target/s
Fri, Mar. 25
Analyze how the volume of
a prism with a fixed height
and surface area changes as
the number of sides
increases.

Pg. 2: FW 2.1:
Surface Area and
Volume of
Prisms

Pg. 3: Puzzle
– Cold Cans

Mon,
Find a strategy to calculate
the volume of any prism
from knowing the area of
the base and the height.

Pg. 4: FW 2.2 –
Calculating
Volume of
Prisms

Pg. 5: Puzzle –
Big, Gray,
California

Identify the twodimensional shapes that can
be created from slicing
three-dimensional shapes.

Pg. 6-9: FW 1.4 –
Scaling Up
Prisms

Pg. 10: SBAC
Review Part 2
– Complete
and Correct
with Zaption

Assess understanding of
Investigation 2 learning
targets.

Partner Quiz

Finish Partner
Quiz for
Homework

Mar. 28
Tues,
Mar. 29
Weds,
Mar. 30
Inv. 2
Classwork
Homework
Self-Assess
Your Learning
Date
CCSS.MATH.CONTENT.7.G.A.3: Describe the two-dimensional figures that
result from slicing three-dimensional figures, as in plane sections of right
rectangular prisms and right rectangular pyramids.
CCSS.MATH.CONTENT.7.G.B.6: Solve real-world and mathematical problems
involving area, volume and surface area of two- and three-dimensional
objects composed of triangles, quadrilaterals, polygons, cubes, and right
prisms.
Parent/Guardian Signature: ________________________________ Due: ______________________________
1
FW 2.1: Surface Area and Volume of Prisms
A. Assume the prisms have a top and a bottom.
Prism Type
Number
Area of
Area of
of Faces
Sides
Top or
(Surfaces) (Lateral SA) Bottom
Formula
(Base)
Total Surface Area
Height
Lateral SA + 2(Base)
Volume
Base x Height
Triangular
93.75 cm2
7.5 cm2
7.6 cm
Square
93.75 cm2
9.8 cm2
7.6 cm
Pentagonal
93.75 cm2
10.8 cm2
7.6 cm
Hexagonal
93.75 cm2
11.3 cm2
7.6 cm
Octagonal
93.75 cm2
11.8 cm2
7.6 cm
B. How do the lateral surface areas of the five prisms compare as the number of faces in the prisms
increases? Explain.
C. How do the total surface areas of the five prisms compare as the number of faces in the prisms increases?
Explain.
D. How do the volumes of the five prisms compare as the number of faces in the prisms increases? Explain.
E. How could you use another identical sheet of paper to make a figure whose volume is greater than the
volume of any of the polygonal prisms in question A? What might it look like?
a. How would the surface area of that figure compare to the surface areas of the polygonal prisms in
Question A?
2
Show all of your work to calculate each volume.
3
FW 2.2: Calculating Volume of Prisms
A. Use these prisms to answer the questions below.
Prism
Area of the Base
Height of the Prism
Volume of Prism
Square Prism
Triangular
Prism
Hexagonal
Prism
1.
How are the volumes of the prisms related?
2. Describe a general strategy for finding the volume of each prism. How does your strategy help you
compare the volumes of the prisms?
B.
1. A triangular prism has a right triangle base with one leg 4 inches and the other leg 7 inches. The height of
the prism is 11 inches. What is its volume?
2. What is the volume of an octagonal prism whose base area is 15 square centimeters and whose height is
4.5 centimeters?
4
Show all of your work to calculate each volume.
5
FW 2.3: Slicing Pyramids and Prisms
1.


The Cube
Using play-doh, create a model of a cube.
Using dental floss, slice through the middle of the cube in a direction perpendicular to the base.
Sketch how you sliced the cube and then sketch and name the
If the slice was made in a different
figure formed by the cross-section.
area (but still perpendicular to the
base), would the shape of the
cross-section be the same or
different?

Put the cube back together and slice through the middle of the cube in a direction parallel to the base.
Sketch how you sliced the cube and then sketch and name the
If the slice was made in a different
figure formed by the cross-section.
area (but still parallel to the base),
would the shape of the crosssection be the same or different?

Put the cube back together and create a cross-section that would make a triangle shape.
Sketch how you sliced the cube to make a triangle.

Try to create other cross-sections from making one slice with as many two-dimensional shapes as you can.
Sketch how you sliced the cube to make each shape or note if it was not possible.
Pentagon
Hexagon
Octagon
Circle
6
2.


Rectangular Prisms
Using play-doh, create a right rectangular prism that is not a cube. The bases of the prism are squares and
the lateral faces are rectangles.
Using dental floss, slice through the middle of the prism in a direction that is perpendicular to the base (and
parallel to the faces).
Sketch how you sliced the prism and then sketch and name the figure
If the slice was made in a
formed by the cross-section.
different area (but still
perpendicular to the base),
would the shape of the crosssection be the same or
different?

Put the prism back together and slice through the middle of the prism in a direction parallel to the base.
Sketch how you sliced the prism and then sketch and name the figure
If the slice was made in a
formed by the cross-section.
different area (but still parallel
to the base), would the shape
of the cross-section be the
same or different?

Put the prism back together and create a cross-section that would make a triangle shape.
Sketch how you sliced the prism to make a triangle.

Try to create other cross-sections from making one slice with as many two-dimensional shapes as you can.
Sketch how you sliced the prism to make each shape or note if it was not possible.
Pentagon
Hexagon
Octagon
Circle
7
3. Cylinders
 Using modeling clay or play-doh, create a cylinder.
 Using a plastic knife or dental floss, slice through the middle of the cylinder in a direction that is
perpendicular to the base.
Sketch how you sliced the prism and then sketch and name the
figure formed by the cross-section.
If the slice was made in a
different area (but still
perpendicular to the base),
would the shape of the crosssection be the same or different?


Put your cylinder back together again before continuing.
Slice through the middle of the cylinder in a direction parallel to the base.
Sketch how you sliced the prism and then sketch and name the
If the slice was made in a
figure formed by the cross-section.
different area (but still parallel
to the base), would the shape of
the cross-section be the same or
different?

Put your cylinder back together and slice through the cylinder in a direction that is neither parallel nor
perpendicular to the base.
Sketch how you sliced the prism and then sketch and name the figure formed by the cross-section.
8
4. Right Rectangular Pyramids
 Using modeling clay or play-doh, create a right rectangular pyramid.
 Using a plastic knife or dental floss, slice through the middle of the model pyramid in a direction that is
perpendicular to the base (and slices through the vertex).
Sketch how you sliced the prism and then sketch
and name the figure formed by the cross-section.
If the slice was made in a different area (but still
perpendicular to the base), would the shape of the
cross-section be the same or different?
Sketch an example of a cross-section made from a
different area.


Put your pyramid back together again before continuing.
Slice through the middle of the model pyramid in a direction parallel to the base.
Sketch how you sliced the prism and then sketch
If the slice was made in a different area (but still
and name the figure formed by the cross-section.
parallel to the base), would the shape of the
cross-section be the same or different?

Put your pyramid back together and slice through the pyramid in a direction that is neither parallel nor
perpendicular to the base.
Sketch how you sliced the prism and then sketch and name the figure formed by the cross-section.
9
SBAC Practice Test – Part 2
?
Question and Answer
Score: ___ / 4
Correct
Answer
1
2
3
4
10