Transcript No Slide Title

Volume of Prisms
1) Defining Volume
2) Volume = lwh
3) Volume = Bh
Created by:
David W. Cummins
Volume
is the
We can begin
by space
stacking
the
units occupies.
in the
thatcubic
a figure
bottom
of the prism
It is measured
in cubic
units.
This prism holds 9 cubic
The
of the given
unitsvolume
in the bottom
layer.
cube can be found by
We can continue to stack
determining how many
these layers until the
cubic units will fit inside the
prism is full.
cube.
This prism holds 3 layers of
9 cubic units for a total of
27 cubic units
3units
3units
3units
1 cubic unit
1unit
V = 27 cubic units
1unit
1unit
Another way to find the volume
of the prism is to use the
3units
formula
h
V = lwh
3units
l
3units
w
where V is volume, l is length,
w is width, and h is height
V = lwh
V = (3)(3)(3)
V = 27 cubic units
This formula works very well for rectangular prisms
Another way to find the volume
of the prism is to use the
3units
formula
h
V = Bh
3units
l
3units
w
Base Area
B = lw
where V is volume, B is the
base area, and h is height
V = Bh
V = (9)(3)
V = 27 cubic units
B = (3)(3)
B = 9 square units
This formula works very well for
non-rectangular prisms
Find the volume of this rectangular prism
7 in
4 in
5 in
OR
Since this is a
rectangular prism
we can use
We could use
V = lwh
The base is a rectangle
we have:
B = lw
V = (5)(4)(7)
B = (5)(4)
in3
B = 20 in2
V = 140
In this case it’s much easier to use
V = lwh
V = Bh
now we use V = Bh
V = (20)(7)
V = 140 in3
Find the volume of this triangular prism
Since this BASE
is a triangular
AREA prism we
must use2
B = 6 cm
5 cm
V = Bh
Now we use
since the base is a triangle we must
Bhtriangle first
find the areaVof=the
where h is theusing:
distance between
4 cm
9 cm
bases.
Bthe
= (1/2)bh
)(9 cm)
(whereVb =&(6
h cm
are2perpendicular)
3
3 cm
54 cm
BV
= =(1/2)(3)(4)
B = (1/2)(12)
B = 6 cm2