Volume of a Rectangular Prism

1
Volume of a Rectangular Prism

• TEKS 6.4 A/B 6.8 A/B
• Lesson 8 9 (2nd 6 Weeks)

2
Volume of a Rectangular Prism

• The amount of space inside the prism.
• Volume is measured in cubic units.
• Formula V lwh
• V in the formula represents volume.
• The variable l represents length of the prism,
  the variable w represents the width, and the
  variable h represents the height.

3
Volume of a Cube

• A cube is a special rectangular prism. The
  length, width, and height of a cube are equal.
• Volume of a cube l x w x h
• s x s x s (s³)

4

• Volume of a cube l x w x h
• s x s x s (s³)
• Hint In order to find a missing dimension, you
  may need to work backwards!

Multiplying the same number or variable three
times is called finding the cube of the number.
5

• The volume of a rectangular prism with a width
  that stay the same but the length and height
  changes is given in the table
• Which expression can be used to find the volume
  of a rectangular prism whose width is 7 units,
  width is w units and length is l units?
• A 7 x l h
• B (7 l) x h
• C
• D 7 x l x h

Width (units) Length (units) Height (units) Volume (cubic units)
7 3 2 42
7 4 3 84
7 9 4 252
7 L W V
1. Lets look at our 6th grade math chart to see
if there is anything to help us.
4 x l
We should find the formula for volume of a
rectangular prism. V lwh
h
6
A 7 x l h B (7 l) x h C D 7 x l x
h
Width (units) Length (units) Height (units) Volume (cubic units)
7 3 2 42
7 4 3 84
7 9 4 252
7 L W V
x
x
x
x
x
x
x
x
2. We know that when variables are next to each
other that it means to multiply. V l x w x h
4 x l
h
3. Lets check to see if that is the formula they
are using.
7
A 7 x l h B (7 l) x h C D 7 x l x
h
Width (units) Length (units) Height (units) Volume (cubic units)
7 3 2 42
7 4 3 84
7 9 4 252
7 L W V
x
x
x
x
x
x
x
x
So it looks like we are multiplying the width by
the length and height. Lets check our answer
choices to see if one of them is doing that.
4 x l
h
We find our choice to be D.
8

• A cube has a side length of 4 inches. Which of
  the following expressions represents the volume
  of the cube?
• A 4³
• B 4 4 4
• C 4 x 4 4
• D 4 x (4 4)

Lets look at our 6th grade math chart to see if
there is anything to help us.
We should find the formula for volume of a
cube. V s³
We know that s³ means s x s x s So if we replace
4 for s we would have 4³ or 4 x 4 x 4
So our answer must be A
9

• The length of a rectangular prism is 8
  units. The ratio of the height to the width is
  43. If the height is 12 units, what expression
  represent the volume of the prism?
• A. V 8 9 12
• B. V 8 x 3 x 12
• C. V 8 x 9 x 12
• D. V 8 x 16 x 12

We know the formula for volume is V lwh.
Looking at the problem we know the length and
height. We are missing the width but since it
says a ratio we can make a ratio table to find
the equivalent width.
x 3
4
12
height
So our answer is C
9
w
3
width
x 3