The surface area of a solid figure is
the sum of the areas of its surfaces. To
help you see all the surfaces of a solid
figure, you can use a net.
A net is the pattern made when the
surface of a solid figure is laid out flat
showing each face of the figure.
Color a Rectangular Prism Net
1. Color the rectangular prism like the
example below: (Blue, Pink, Green)
Create a Rectangular Prism Net
1. Cut out the rectangular prism net along
the solid black outside line.
2. DO NOT cut off the flaps.
3. Fold along the dotted lines. Make sure
you make a good STRAIGHT crease.
4. Find the surface area of each rectangle
and write it on the back of each rectangle.
5. Find the total surface area and write it the
table.
Surface Area Table
Faces
Green Face 1
Green Face 2
Pink Face 1
Pink Face 2
Blue Face 1
Blue Face 2
Total
Surface Area cm²
10-8 Finding
Insert Lesson
VolumeTitle Here
Vocabulary
volume
Course 1
10-8 Finding Volume
Volume is the number of cubic
units needed to fill a space.
Course 1
# of cubes in a Rectangular
Prism
6. Lay the rectangular prism face down, so
that the folds fold up.
7. Lay 1 layer of cubes down.
8. How many cubes fit on the first layer?
Fill in your answer.
9. Start the 2nd layer of cubes & fill in your
answer.
# of cubes in Layer 1: ________________________________
# of cubes in Layer 2: ________________________________
Volume of Rectangular Prism
10. How many layers can you fit?
11. The number of layers is the height.
Write in your answer.
12. What is the total volume of the
rectangular prism? Write in your answer.
13. Can you think of a formula that we can
use EVERY time so that we don’t have to do
this much work when we want to find the
volume of a prism?
10-8 Finding Volume
It takes 10, or 5 · 2,
centimeter cubes to cover
the bottom layer of this
rectangular prism.
There are 3 layers of 10
cubes each. It takes 30, or
5 · 2 · 3, cubes to fill the
prism.
The volume of the prism is 5 cm · 2 cm · 3 cm = 30 cm3.
Course 1
10-8 Finding Volume
Additional Example 1: Finding the Volume of a
Rectangular Prism
Find the volume of the rectangular prism.
13 in.
26 in.
11 in.
V = lwh
V = 26
•
Write the formula.
11
•
V = 3,718 in3
Course 1
13
l = 26; w = 11; h = 13
Multiply.
10-8 Finding Volume
Try This: Example 1
Find the volume of the rectangular prism.
16 in.
29 in.
12 in.
V = lwh
V = 29
•
Write the formula.
12
•
V = 5,568 in3
Course 1
16
l = 29; w = 12; h = 16
Multiply.
10-8 Finding Volume
To find the volume of any prism,
you can use the formula V= Bh,
where B is the area of the base,
and h is the prism’s height. So, to
find the volume of a triangular
prism, B is the area of the
triangular base and h is the height
of the prism.
Course 1
10-8 Finding Volume
Additional Example 2A: Finding the Volume of
a Triangular Prism
Find the volume of each triangular prism.
A.
V = Bh
1
__
V = ( • 3.9
2
•
V = 10.14 m3
Course 1
1.3)
•
4
Write the formula.
1
B = __ • 3.9 • 1.3; h = 4.
2
Multiply.
10-8 Finding Volume
Additional Example 2B: Finding the Volume of
a Triangular Prism
Find the volume of the triangular prism.
B.
V = Bh
1
__
V = ( • 6.5
2
V = 136.5 ft
Course 1
3
•
7)
•
6
Write the formula.
1
B = __ • 6.5 • 7; h = 6.
2
Multiply.
10-8 Finding Volume
Try This: Example 2A
Find the volume of each triangular prism.
A.
7m
1.6 m
4.2 m
V = Bh
1
__
V = ( • 4.2
2
•
V = 23.52 m3
Course 1
1.6)
•
7
Write the formula.
1
B = __ • 4.2 • 1.6; h = 7.
2
Multiply.
10-8 Finding Volume
Try This: Example 2B
Find the volume of each triangular prism.
B.
9 ft
5 ft
4.5 ft
V = Bh
1
__
V = ( • 4.5
2
•
V = 101.25 ft3
Course 1
9)
•
5
Write the formula.
1
B = __ • 4.5 • 9; h = 5.
2
Multiply.
10-8 Finding Volume
Additional Example 3: Problem Solving
Application
Suppose a facial tissue company ships 16 cubic
tissue boxes in each case. What are the possible
dimensions for a case of tissue boxes?
1
Understand the Problem
The answer will be all possible dimensions
for a case of 16 cubic boxes.
List the important information:
• There are 16 tissue boxes in a case.
• The boxes are cubic, or square prisms.
Course 1
10-8 Finding Volume
Additional Example 3 Continued
2
Make a Plan
You can make models using cubes to find the
possible dimensions for a case of 16 tissue
boxes.
Course 1
10-8 Finding Volume
Additional Example 3 Continued
3
Solve
You can make models using cubes to find the
possible dimensions for a case of 16 cubes.
The possible dimensions for a case of 16
cubic tissue boxes are the following: 1 • 1
16, 1 • 2 • 8, 1 • 4 • 4, and 2 • 2 • 4 .
Course 1
•
10-8 Finding Volume
Additional Example 3 Continued
4
Look Back
Notice that each dimension is a factor of 16.
Also, the product of the dimensions (length •
width • height) is 16, showing that the
volume of each case is 16 cubes.
Course 1
10-8 Finding Volume
Try This: Example 3
Suppose a paper company ships 12 cubic
boxes of envelopes in each case. What are the
possible dimensions for a case of envelope
boxes?
1 Understand the Problem
The answer will be all possible dimensions
for a case of 12 cubic boxes.
List the important information:
• There are 12 envelope boxes in a case.
• The boxes are cubic, or square prisms.
Course 1
10-8 Finding Volume
Try This: Example 3 Continued
2
Make a Plan
You can make models using cubes to find the
possible dimensions for a case of 12 boxes of
envelopes.
Course 1
10-8 Finding Volume
Try This: Example 3 Continued
3
Solve
You can make models using cubes to find the
possible dimensions for a case of 12 cubes.
The possible dimensions for a case of 24 cubic
envelope boxes are the following: 1 • 1 • 12, 1
• 2 • 6, 1 • 3 • 4, and 2 • 2 • 3.
Course 1
10-8 Finding Volume
Try This: Example 3 Continued
4
Look Back
Notice that each dimension is a factor of 12.
Also, the product of the dimensions (length •
width • height) is 12, showing that the
volume of each case is 12 cubes.
Course 1
10-8 Finding
Insert Lesson
VolumeTitle Here
Lesson Quiz
Find the volume of each figure.
1. rectangular prism with length 20 cm, width 15
cm, and height 12 cm
3,600 cm3
2. triangular prism with a height of 12 cm and a
triangular base with base length 7.3 cm and
height 3.5 cm 153.3 cm3
3. Find the volume of the figure shown.
38.13 cm3
Course 1