Learning Resources ler 4331 Volume Estimation, Volume Formulas, Terminology of Solid Geometry

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 filling each shape with water using a graduated cylinder and recording the results beside each listed shape.

Volume Formulas			r – radius			b – base
v – volume
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		(1 ⁄2	bh) h
Square pyramid: v = 1	⁄3	(lw) h	Triangular pyramid: v =	1 ⁄3
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 flat or curved hemisphere one half of any sphere

polyhedron solid figure 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 fill 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.