®
Activity Guide
LER 4331
Ages
+
8
Grades
+
3
Cube Sphere
Triangular prism
Cone
Hemisphere Cylinder
Pentagonal prismRectangular prism
Square pyramid
Triangular pyramid
Volume Estimation
Introduce concepts of volume relationship between solid shapes with this set of 14 large
View-Thru Geometric Solids. Use the shapes to estimate, measure and compare volumes
in a small group or demonstration setting.
Have students list, from least to greatest, the estimated volume of each solid. Students should
check estimates by calculating the volume or lling each shape with water using a graduated
cylinder and recording the results beside each listed shape.
Volume Formulas
v – volume r – radius b – base
l – length w – width h – height
s – side length of base
a – apothem (length from the center of a polygon to one side)
4
Cube: v = l ³ Sphere: v = (
Cone: v = 1⁄3 (πr²h) Cylinder: v = πr²h
Rectangular prism: v = lwh Hemisphere: v = (2⁄3) πr ³
Square pyramid: v = 1⁄3 (lw) h Triangular pyramid: v = 1⁄3 (1⁄2 bh) h
Pentagonal prism: v = 5⁄2 ash Triangular prism: v = (1⁄2 bh) h
⁄3) πr ³
Terminology of Solid Geometry
base face of a geometric shape; bases of the View-Thru geometric solids are blue
cylinder two congruent, parallel circular bases and a single curved, lateral face
edge intersection of two faces of a polyhedron where they meet at a line
face polygon surface of a polyhedron; shapes in this set are either at or curved
hemisphere one half of any sphere
polyhedron solid gure with a polygon face
prism polyhedron with two congruent, parallel bases and rectangles for the remaining
faces; named for the shape of its bases
pyramid polyhedron with one base and triangles for the remaining faces; named for the
shape of its bases
sphere the set of all points in space equidistant from a given point called the center
vertex intersection of three or more faces of a polyhedron where they meet at a point,
or corner
Working with the View-Thru
Geometric Solids to Measure Volume
The set of 14 View-Thru Geometric Solids is ideal for measuring and comparing volume
relationships between the various solid shapes. In order to facilitate volume measurement
relationships, set up the following materials at a geometry center or centers in your classroom:
Materials: View-Thru Geometric Solids
1000 Milliliters of plastic ll
Set of 2 funnels
Chart of the 14 solids and their characteristics
Paper and pencil/pen
Procedure: Have students estimate the volume of each of the 14 View-Thru Geometric
Solids by listing them on a sheet of paper from largest volume to smallest
volume.
Volume is expressed in cubic units of measurement: inches, feet, yards, miles,
milliliters, centimeters, decimeters, meters, kilometers, etc.
Using the funnel, ll the 1-liter graduated cylinder with plastic ll.
Remove the base of the chosen solid and ll it with the plastic ll. Note the
amount of ll required. Repeat two or three times to ensure accuracy.
Repeat the process with all of the shapes.
Have the students evaluate their data by listing the solids in descending order
from most volume to least volume. Compare completed list with original
estimation.
Discuss: What other materials could be used for the measurements?
What relationships exist between the various solids? How does the volume
of the cube compare to the volume of the square pyramid? Explain any other
comparisons derived from the data.
Characteristics of Geometric Solids
Work with the students to create a chart like the one below to record their own
observations:
View-Thru®
Geometric Solids
1 Large Cube
2 Small Cube
3 Large Rectangle
4 Small Rectangle
5 Pentagonal Prism
6 Large Triangular Prism
7 Small Triangular Prism
8 Square Pyramid
9 Triangular Pyramid
10 Large Cylinder
11 Small Cylinder
12 Cone
Shape
of Base(s)
Number
of Faces
Number
of Vertices
Number
of Edges
13 Sphere
14 Hemisphere
Euler’s Formula
Euler’s Formula is named after Swiss mathematician Leonard Euler. In the mid-eighteenth
century, Euler discovered that for any polyhedron, F + V = E + 2. In the formula, F represents
the number of faces, V represents the number of vertex points, and E represents the number of
edges. For example, a cube has 6 faces, 8 vertex points, and 12 edges.
F + V = E + 2
6 + 8 = 12 + 2
Have the students use their data from the preceding chart to discover Euler’s Formula. Euler’s
Formula is true for the rst nine solids listed in the table.
Intervention Strategies
Scaffolded Instruction: Before providing formulas to students, instead provide the
denitions of perimeter and area, and opportunities to solve problems that allow students
to gain data leading to the use of a formula. Begin with two-dimensional shapes before
advancing to three-dimensional solids.
Directed Orientation: Use different household items that resemble a cube, cone, sphere,
cylinder, pyramid, or prism. Have students sort the items by different attributes you provide.
Then, introduce the formal shapes and have students match the shapes to the corresponding
household items.
Free Exploration: Have students ll the solids with rice or water to explore properties of
volume. Encourage students to make estimations and compare which shapes are able to hold
more or less than the others.
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