Name: ___________________________________
Date: _________________
VOLUME OF PRISMS AND CYLINDERS
HONORS GEOMETRY
PRISM VOLUME – THE STACKING PRINCIPLE
A powerful technique to use when calculating the volume of a prism is stacking. For example, the stack of
CD’s is a solid made up of many square cases upon each other or the volume of paper made up of stacking
many rectangular sheets (8 ½ by 11) upon each other or money or coasters. All of these cross sections have a
height dimension but if we make that height infinitesimal small we begin again to approximate the relationship
more accurately.
A Stack of CD Cases
Cross Section: Square
A Stack of Paper
Cross Section:
Rectangle
A Stack of Money
Cross Section:
Rectangle
A Stack of Coasters
Cross Section: Squares
Because in a prism we have two translated congruent bases in parallel planes (the bases), all of the cross
sections are also identical to the bases. So to calculate the volume of a prism we calculate the area of the base
and then multiply it by the height of the prism – thus stacking that area on top of itself to fill in the volume of
the shape.
The stacking of congruent parallel cross sections allows us to create a formula for the volume of prism.
VolumePRISM = Bh, where B is the area of the base and h is the height of the prism.
GEOMETRY- UNIT #6 – AREA AND VOLUME– LESSON #10
Example 1: Find the volume of each of the following prisms.
(a)
(b)
(c)
(d)
GEOMETRY- UNIT #6 – AREA AND VOLUME– LESSON #10
CYLINDER VOLUME – THE STACKING PRINCIPLE
The same stacking technique works great for cylinders as
well. All cross section parallel to the base are all congruent
circles and so using the same technique we are able to
determine the formula to be:
AREACYLINDER = Bh = r2h
Example 2: Find the volume of each of the following cylinders.
Example #1
Example #2
GEOMETRY- UNIT #6 – AREA AND VOLUME– LESSON #10
Example #3
Name: ___________________________________
Date: _________________
VOLUME OF PRISMS AND CYLINDERS
HONORS GEOMETRY HOMEWORK
1. The same rectangular prism is provided three times below but in each instance a DIFFERENT BASE
has been highlighted. Calculate the volume for each but change the base dimensions.
a)
b)
c)
What do you notice about the volumes of these three examples? Why didn’t changing the base change the
volume?
2. Determine the volume of the prisms or cylinders. (Lines that appear perpendicular are perpendicular.)
a)
b)
c)
d)
GEOMETRY- UNIT #6 – AREA AND VOLUME– LESSON #10
e)
f)
g)
h)
i)
Inner Radius = 2 cm
j)
GEOMETRY- UNIT #6 – AREA AND VOLUME– LESSON #10
k)