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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)
Cube: v = l ³ Sphere: v = (
4
⁄3) πr ³
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
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.