Today we will explore the Essential Question, “What is the process for using volume of a
right rectangular prism to solve problems?"
The focus of this lesson is on solving problems involving volume of a right rectangular
prism. A right rectangular prism is a box-shaped figure that looks like the figure shown.
The edges are called the length, width, and height and are denoted l, w, and h.
h
l
w
When building or covering a box, it is necessary to find the surface area. When filling the
box, it is necessary to find the volume of the box.
The formula for the volume (V) of a right rectangular prism is given on the FCAT formula
sheet.
V  lwh
Example 1: Two rectangular boxes have the
same height and the same length, but different
widths, as shown in the figure. The difference
in the volumes of Box B and Box A is 360 cubic
centimeters. What is h, the height of each box
in centimeters?
Box A:
h
A
9 cm
h
8 cm
B
8 cm
12 cm
Box B:
l  9, w  8, h  ?
V  l  w h
l  12, w  8, h  ?
V  l  w h
V  89 h
V  8 12  h
V  72h
V  96h
96h  72h  360
24h  360
24h 360

24
24
h  15
Therefore, the height of each box is 15 centimeters.
Example 2: A company needs to build a box whose dimensions
can change but are always related as shown in the figure. Find a
simplified formula, in terms of x, for the volume of the box.
x+3
l  x, w  2x, h  x  3
V  lwh
V  x 2x x  3


V  2x x  3
2
V  2x  6x
3
2
2x
x
Guided Practice Problems:
1. A shopping carton for computer parts is in the shape of a cube that measures
10 inches on each edge. In each of its bottom corners, the carton has one
foam cube. Each foam cube measures 2 inches on an edge, as shown in the
diagram. What is the volume, in cubic inches, of the empty space in the
shipping carton when the 4 foam cubes are in the box?
Shopping Carton:
V lwh
V 101010
V 1000
Small foam cube:
V  lwh
V  2 2 2
V 8
4 Small foam cubes:
Volume of empty space:
V = 4(8) = 32
1000 – 32 = 968
2. Two rectangular boxes have the same height and the same length, but different widths, as shown
in the figure. The difference in the volumes of Box B and Box A is 36 cubic inches. What is h, the
height of each box in inches?
h inches
h inches
B
A
2 inches
3 inches
2 inches
5 inches
Box B:
Box A:
l  3, w  2, h  ?
l  5, w  2, h  ?
V  l  w h
V  l  w h
V  3 2 h
V  6h
V  5 2  h
V 10h
The height of each box is 9 inches.
10 h  6 h  36
4 h  36
4 h 36

4
4
h9
3. The diagram shows the dimensions of the cargo space in a moving van. What is the maximum
volume of cargo, in cubic feet, that can fit in the van?
3 ft
The van is made up of a large prism
6 ft
adjoined to a small prism.
3
Small prism:
8
3 ft
Large prism:
19 ft
9
3
l  8, w  3, h  3
V  l  w h
V  833
l  8, w  19, h  9
V  l  wh
V  8 19  9
V  72
V  1368
8
19
The volume of the cargo space in the van is the sum of the volumes of the two prisms.
Therefore the total volume is 72 + 1368 or 1440 cubic feet.
8 ft
4. Find a simplified formula for the volume of the box shown in the diagram below. Show your
work.
l  x, w  3 x, h  x  2
V  l  wh
height = x +2
length = x
V  x  3 x  ( x  2)
V  3 x 2  ( x  2)
V  3x3  6 x 2
width = 3x
Independent Practice: Complete the two sample questions finding the volume of a rectangular
prism. Remember that tomorrow we will have our mini-assessment on this topic. You should
prepare for this assessment by reviewing the examples, the guided practice problems and these
problems.
1. Find a simplified formula for the volume of the box shown in the diagram.
Show your work.
l  5, w  x, h  2 x  3
V  l  w h
V  5  x  (2 x  3)
V  5 x(2 x  3)
length = 5
height = 2x + 3
width = x
V  10 x 2  15 x
2. As shown in the diagram, a box with a square base is increased in size. The base remains
the same but the height is increased from 20 inches to 40 inches. How many additional
cubic inches are contained in the volume of the larger box?
Small Prism: l  10, w  10, h  20
V  l  w h
V  10 10  20
V  2000
Large Prism: l  10, w  10, h  40
V  l  w h
V  10 10  40
V  4000
4000 – 2000 = 2000 additional cubic inches in the larger box.
40”
20”
10”
10”