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room on the outside of a shape, and volume is the amount of space inside a
shape. Discuss the importance of measuring volume, giving such examples as
knowing how much water a pool will hold, how much air fills a SCUBA tank,
or how much cement fits in a cement mixer. Ask students for other examples.
Students will benefit from practice with building, measuring, and filling
containers to understand volume. Each shape has openings in the base and
can be filled with water, sand, rice, or other materials. By filling one shape
and pouring its contents into another shape, students can explore volume
relationships between shapes. If you intend to have students perform exact
measurements using a graduated cylinder, be sure they are comfortable
reading the bottom edge of the water level, or meniscus.
Note: The bottoms of each shape are not removable.
Challenge students to estimate the volume of each shape and place them in
order from largest to smallest volume. You may want to allow students to
fill their shapes to make more accurate estimations. As you introduce the
formulas for finding the volume of each shape, encourage students to refer
to the shapes for reference. You may wish to distribute copies of the table
on page 2 for reference.
Once you have finished your discussion, students can mathematically
calculate the volume of each shape to confirm the accuracy of their initial
guesses about volume.
These models were built using the metric system. Although they can be used
with any measurement system, metric is easiest. Because of the thickness of
the plastic, measurements between students might be slightly “off,” depending
on if they measure from the inside edges or the outside edges. If students round
to the nearest centimeter, this will not be a problem.
Volume Formulas
Prism
Finding the volume of a general prism is simply a matter of multiplying the
area of the base times the height of the prism:
Volume
general prism
= A
××
H
A = Area of the base.
H = Height of the prism.
The formula for the area of the base of the prism
depends upon the shape
of the base.
Rectangular Prism
Volume
rectangular prism
= A
××
H
5
H
w
l