Our learning goal is to be able to solve
for perimeter, area and volume.
Learning Goal Assignments
1.Perimeter and Area of Rectangles and Parallelograms
2.Perimeter and Area of Triangles and Trapezoids
3.The Pythagorean Theorem
4.Circles
5.Drawing Three-Dimensional figures
6.Volume of Prisms and Cylinders
7.Volume of Pyramids and Cones
8.Surface Area of Prisms and Cylinders
9.Surface Area of Pyramids and Cones
10.Spheres
6-6 Volume of Prisms and Cylinders
Learning Goal Assignment
Learn to find the
volume of prisms
and cylinders.
Pre-Algebra
6-6 Volume of Prisms and Cylinders
Pre-Algebra HOMEWORK
Page
#
Pre-Algebra
6-6
ofof
Prisms
and
Cylinders
6-6 Volume
Volume
Prisms
and
Cylinders
Warm Up
Problem of the Day
Lesson Presentation
Pre-Algebra
Pre-Algebra
6-6 Volume of Prisms and Cylinders
Warm Up
Make a sketch of a closed book using
two-point perspective.
Pre-Algebra
6-6 Volume of Prisms and Cylinders
Warm Up
Make a sketch of a closed book using
two-point perspective.
Possible answer:
Pre-Algebra
6-6 Volume of Prisms and Cylinders
Problem of the Day
You are painting identical wooden cubes
red and blue. Each cube must have 3
red faces and 3 blue faces. How many
cubes can you paint that can be
distinguished from one another? only 2
Pre-Algebra
6-6 Volume of Prisms and Cylinders
Learning Goal Assignment
Learn to find the
volume of prisms
and cylinders.
Pre-Algebra
6-6 Volume of Prisms and Cylinders
Vocabulary
prism
cylinder
Pre-Algebra
6-6 Volume of Prisms and Cylinders
A prism is a three-dimensional figure
named for the shape of its bases. The two
bases are congruent polygons. All of the
other faces are parallelograms. A cylinder
has two circular bases.
Pre-Algebra
6-6 Volume of Prisms and Cylinders
Remember!
If all six faces of a rectangular prism are
squares, it is a cube.
Rectangular
prism
Triangular
prism
Height
Height
Height
Base
Pre-Algebra
Cylinder
Base
Base
6-6 Volume of Prisms and Cylinders
VOLUME OF PRISMS AND CYLINDERS
Words
Prism: The
volume V of a
prism is the area
of the base B
times the height
h.
Cylinder: The
volume of a
cylinder is the area
of the base B times
the height h.
Pre-Algebra
Numbers
B = 2(5)
= 10 units2
V = 10(3)
Formula
V = Bh
= 30 units3
B = p(22)
= 4p units2
V = (4p)(6) = 24p
 75.4 units3
V = Bh
= (pr2)h
6-6 Volume of Prisms and Cylinders
Helpful Hint
Area is measured in square units. Volume is
measured in cubic units.
Pre-Algebra
6-6 Volume of Prisms and Cylinders
Additional Example 1A: Finding the Volume of
Prisms and Cylinders
Find the volume of each figure to the nearest
tenth.
A. A rectangular prism with base 2 cm by 5
cm and height 3 cm.
B = 2 • 5 = 10 cm2
V = Bh
= 10 • 3
= 30 cm3
Pre-Algebra
Area of base
Volume of a prism
6-6 Volume of Prisms and Cylinders
Try This: Example 1A
Find the volume of the figure to the nearest
tenth.
A. A rectangular prism with base 5 mm by 9
mm and height 6 mm.
B = 5 • 9 = 45 mm2
V = Bh
= 45 • 6
= 270 mm3
Pre-Algebra
Area of base
Volume of prism
6-6 Volume of Prisms and Cylinders
Additional Example 1B: Finding the Volume of
Prisms and Cylinders
Find the volume of the figure to the nearest
tenth.
B.
4 in.
B = p(42) = 16p in2 Area of base
V = Bh
12 in.
= 16p • 12
Volume of a
cylinder
= 192p  602.9 in3
Pre-Algebra
6-6 Volume of Prisms and Cylinders
Try This: Example 1B
Find the volume of the figure to the nearest
tenth.
B.
B = p(82)
8 cm
= 64p cm2
V = Bh
15 cm
Volume of a cylinder
= (64p)(15) = 960p
 3,014.4 cm3
Pre-Algebra
Area of base
6-6 Volume of Prisms and Cylinders
Additional Example 1C: Finding the Volume of
Prisms and Cylinders
Find the volume of the figure to the nearest
tenth.
1
• 6 • 5 = 15 ft2 Area of base
2
V = Bh
Volume of a prism
= 15 • 7
C.
5 ft
B=
7 ft
6 ft
Pre-Algebra
= 105 ft3
6-6 Volume of Prisms and Cylinders
Try This: Example 1C
Find the volume of the figure to the nearest
tenth.
C.
1
B=
• 12 • 10 Area of base
2
= 60 ft2
10 ft
V = Bh
14 ft
12 ft
Pre-Algebra
= 60(14)
= 840 ft3
Volume of a prism
6-6 Volume of Prisms and Cylinders
Additional Example 2A: Exploring the Effects of
Changing Dimensions
A juice box measures 3 in. by 2 in. by 4 in.
Explain whether tripling the length, width, or
height of the box would triple the amount of
juice the box holds.
The original box has a volume of 24 in3. You could
triple the volume to 72 in3 by tripling any one of the
dimensions. So tripling the length, width, or height
would triple the amount of juice the box holds.
Pre-Algebra
6-6 Volume of Prisms and Cylinders
Try This: Example 2A
A box measures 5 in. by 3 in. by 7 in. Explain
whether tripling the length, width, or height of
the box would triple the volume of the box.
The original box has a volume of (5)(3)(7) = 105 cm3.
V = (15)(3)(7) = 315 cm3
Tripling the length would
triple the volume.
Pre-Algebra
6-6 Volume of Prisms and Cylinders
Try This: Example 2A
A box measures 5 in. by 3 in. by 7 in. Explain
whether tripling the length, width, or height of
the box would triple the volume of the box.
The original box has a volume of (5)(3)(7) = 105 cm3.
V = (5)(3)(21) = 315 cm3
Tripling the height would
triple the volume.
Pre-Algebra
6-6 Volume of Prisms and Cylinders
Try This: Example 2A
A box measures 5 in. by 3 in. by 7 in. Explain
whether tripling the length, width, or height of
the box would triple the volume of the box.
The original box has a volume of (5)(3)(7) = 105 cm3.
V = (5)(9)(7) = 315 cm3
Tripling the width would
triple the volume.
Pre-Algebra
6-6 Volume of Prisms and Cylinders
Additional Example 2B: Exploring the Effects of
Changing Dimensions
A juice can has a radius of 2 in. and a height
of 5 in. Explain whether tripling the height of
the can would have the same effect on the
volume as tripling the radius.
By tripling the height, you would triple the volume.
By tripling the radius, you would increase the
volume to nine times the original.
Pre-Algebra
6-6 Volume of Prisms and Cylinders
Try This: Example 2B
A cylinder measures 3 cm tall with a radius of
2 cm. Explain whether tripling the radius or
height of the cylinder would triple the amount
of volume.
The original cylinder has a volume of 4p • 3 = 12p cm3.
V = 36p • 3 = 108p cm3
By tripling the radius,
you would increase the
volume nine times.
Pre-Algebra
6-6 Volume of Prisms and Cylinders
Try This: Example 2B
A cylinder measures 3 cm tall with a radius of
2 cm. Explain whether tripling the radius or
height of the cylinder would triple the amount
of volume.
The original cylinder has a volume of 4p • 3 = 12p cm3.
V = 4p • 9 = 36p cm3
Tripling the height would
triple the volume.
Pre-Algebra
6-6 Volume of Prisms and Cylinders
Additional Example 3: Construction Application
A section of an airport runway is a rectangular
prism measuring 2 feet thick, 100 feet wide, and
1.5 miles long. What is the volume of material
that was needed to build the runway?
length = 1.5 mi = 1.5(5280) ft
= 7920 ft
width = 100 ft
height = 2 ft
V = 7920 • 100 • 2 ft3
= 1,584,000 ft3
Pre-Algebra
The volume of material
needed to build the
runway was 1,584,000 ft3.
6-6 Volume of Prisms and Cylinders
Try This: Example 3
A cement truck has a capacity of 9 yards3 of
concrete mix. How many truck loads of concrete to
the nearest tenth would it take to pour a concrete
slab 1 ft thick by 200 ft long by 100 ft wide?
B = 200(100)
= 20,000 ft2
V = 20,000(1)
= 20,000 ft3
20,000
27 ft3 = 1 yd3
 740.74 yd3
27
740.74
= 82.3 Truck loads
9
Pre-Algebra
6-6 Volume of Prisms and Cylinders
Additional Example 4: Finding the Volume of
Composite Figures
Find the volume
of the the barn.
Volume of
barn
=
Volume of
rectangular +
prism
Volume of
triangular
prism
1
(40)(10)(50)
2
= 30,000 + 10,000
V = (40)(50)(15) +
= 40,000 ft3
The volume is 40,000 ft3.
Pre-Algebra
6-6 Volume of Prisms and Cylinders
Try This: Example 4
Find the volume of the figure.
Volume of
barn
=
=
5 ft
=
4 ft
8 ft
Pre-Algebra
3 ft
Volume of
rectangular +
prism
Volume of
triangular
prism
1
(8)(3)(4) +
(5)(8)(3)
2
96
+
V = 156 ft3
60
6-6 Volume of Prisms and Cylinders
Lesson Quiz
Find the volume of each figure to the
nearest tenth. Use 3.14 for p.
1.
10 in.
12 in.
942 in3
2.
12 in.
8.5 in.3 in.
306 in3
3.
2 in.
10.7 in.
15 in.
160.5 in3
4. Explain whether doubling the radius of the
cylinder above will double the volume.
No; the volume would be quadrupled because
you have to use the square of the radius to
find the volume.
Pre-Algebra