8-8 Volume of Prisms and Cylinders
Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
8-8 Volume of Prisms and Cylinders
Warm Up
Identify the figure described.
1. two triangular faces and the other faces in the
shape of parallelograms
triangular prism
2. one hexagonal base and the other faces in the
shape of triangles hexagonal pyramid
3. one circular base and a curved lateral surface that
forms a vertex cone
8-8 Volume of Prisms and Cylinders
Problem of the Day
How can you cut the rectangular prism into
8 pieces of equal volume by making only 3
straight cuts?
8-8 Volume of Prisms and Cylinders
Sunshine State Standards
MA.7.G.2.1 Justify and apply formulas for…
volume of…prisms [and] cylinders…
Also MA.7.G.2.2
8-8 Volume of Prisms and Cylinders
Vocabulary
volume
8-8 Volume of Prisms and Cylinders
Any three-dimensional figure can be filled
completely with congruent cubes and parts of
cubes. The volume of a three-dimensional
figure is the number of cubes it can hold. Each
cube represents a unit of measure called a
cubic unit.
8-8 Volume of Prisms and Cylinders
To find the volume of a rectangular prism,
you can count cubes or multiply the lengths
of the edges.
8-8 Volume of Prisms and Cylinders
8-8 Volume of Prisms and Cylinders
Additional Example 1A: Using a Formula to Find the
Volume of a Prism
Find the volume of the figure.
V = Bh
Use the formula.
The base is a square: B = 4  4 = 16.
V = 16  12 Substitute for B and h.
V = 192
Multiply.
The volume of the prism is 192 ft3.
8-8 Volume of Prisms and Cylinders
Additional Example 1B: Using a Formula to Find the
Volume of a Prism
Find the volume of the figure.
V = Bh
Use the formula.
The base is a triangle: B = 1/2  16  6 = 48.
V = 48  8 Substitute for B and h.
V = 384
Multiply.
The volume of the triangular prism is 384 yd3.
8-8 Volume of Prisms and Cylinders
Check It Out: Example 1A
Find the volume of each figure to the nearest
tenth.
b = 6.3(8) = 50.4
V = Bh = 50.4(6.3) = 317.52
≈ 317.5 ft3.
8-8 Volume of Prisms and Cylinders
Check It Out: Example 1B
Find the volume of each figure to the nearest
tenth.
V=
Bh
1 (13)(10) = 65
2
V = (65)(50) = 3250
B=
≈
3250 m3.
8-8 Volume of Prisms and Cylinders
Reading Math
Any unit of measurement with an exponent of 3
is a cubic unit. For example, m3 means “cubic
meter” and in3 means “cubic inch.”
8-8 Volume of Prisms and Cylinders
Finding the volume of a cylinder is similar to finding
the volume of a prism.
8-8 Volume of Prisms and Cylinders
Additional Example 2: Using a Formula to Find the
Volume of a Cylinder
A can of tuna is shaped like a cylinder. Find its
volume to the nearest tenth. Use 3.14 for .
V = r2h
Use the formula.
The radius of the cylinder is 5 m, and
the height is 4.2 m
V  3.14 · 52 · 4.2 Substitute for r and h.
V  329.7
Multiply.
The volume is about 329.7 m3.
8-8 Volume of Prisms and Cylinders
Check It Out: Example 2
Find the volume of the cylinder to the nearest
tenth. Use 3.14 for .
7 ft
3.8 ft
V = r2h  (3.14)(7)2(3.8)
 584.668
 584.7 ft3.
8-8 Volume of Prisms and Cylinders
Additional Example 3: Finding The Volume of a
Composite Figure
Find the volume of the composite figure to the
nearest ft. Use 3.14 for .
Volume of
Volume of
Volume
a
+ triangular
=
of
composite
prism
prism
figure
+
V
=
V

(4)(6)(12) + (½)(4)(6) · (6)
V

288 + 72
V

360 ft3
Bh
Bh
8-8 Volume of Prisms and Cylinders
Check It Out: Example 3A
Assume that the prism from Exercise 1a has
been stacked on top of the cylinder from
Exercise 2. Find the volume of the composite
figure to the nearest tenth. Use 3.14 for .
V

Bh +  r2h  317.5 + 584.7

902.2

902.2 ft3
8-8 Volume of Prisms and Cylinders
Check It Out: Example 3B
The triangular faces of a triangular prism have
a height of 5 m and a base of 8 m. The height
of the prism is 10 m. The triangular prism is
connected to a cylinder. The height of the
cylinder is 4 m and the radius is 6 m. Find the
volume of the composite figure to the nearest
tenth. Use 3.14 for .
V  Bh +  r2h
B  1 (8)(5) = 20
2
V  (20)(10) + (3.14)(6)2 (4)  652.16
 652.2 m3
8-8 Volume of Prisms and Cylinders
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
8-8 Volume of Prisms and Cylinders
Lesson Quiz
1. Find the volume of the prism.
792 cm3
2. A storage tank is shaped like a
cylinder. Find its volume to the
nearest tenth. Use 3.14 for .
4,069.4 cm3
3. Find the volume of the composite figure.
216 in3
8-8 Volume of Prisms and Cylinders
Lesson Quiz for Student Response Systems
1. Identify the volume of the prism.
A. 35 cm3
B. 95 cm3
C. 133 cm3
D. 665 cm3
8-8 Volume of Prisms and Cylinders
Lesson Quiz for Student Response Systems
2. A piece of wood is shaped like a cylinder. Find its
volume to the nearest tenth. Use 3.14 for .
A. 5849.8 cm3
B. 1950 cm3
C. 414 cm3
D. 207 cm3