Volume of Prisms and Cylinders

1
6-6
Volume of Prisms and Cylinders
Warm Up
Problem of the Day
Lesson Presentation
2
Warm Up Make a sketch of a closed book using
two-point perspective.
3
Warm Up Make a sketch of a closed book using
two-point perspective.
Possible answer
Math
4
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
5
Learn to find the volume of prisms and cylinders.
6
Vocabulary
prism cylinder
7
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.
8
Rectangular prism
Cylinder
Triangular prism
Height
Height
Height
Base
Base
Base
9
VOLUME OF PRISMS AND CYLINDERS
B 2(5)
10 units2
V Bh
V 10(3)
30 units3
B p(22)
V Bh
4p units2
(pr2)h
V (4p)(6) 24p
? 75.4 units3
10
(No Transcript)
11
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
Area of base
Volume of a prism
V Bh
10 3
30 cm3
12
Additional Example 1B Finding the Volume of
Prisms and Cylinders
Find the volume of the figure to the nearest
tenth.
B.
B p(42) 16p in2
Area of base
4 in.
Volume of a cylinder
V Bh
12 in.
16p 12
192p ? 602.9 in3
13
Additional Example 1C Finding the Volume of
Prisms and Cylinders
Find the volume of the figure to the nearest
tenth.
C.
Area of base
5 ft
V Bh
Volume of a prism
15 7
105 ft3
7 ft
6 ft
14
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
Area of base
Volume of prism
V Bh
45 6
270 mm3
15
Try This Example 1B
Find the volume of the figure to the nearest
tenth.
B p(82)
Area of base
B.
8 cm
64p cm2
Volume of a cylinder
V Bh
15 cm
(64p)(15) 960p
? 3,014.4 cm3
16
Try This Example 1C
Find the volume of the figure to the nearest
tenth.
C.
Area of base
10 ft
60 ft2
Volume of a prism
V Bh
60(14)
14 ft
840 ft3
12 ft
17
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.
18
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.
19
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.
20
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.
21
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.
22
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 4? 3
12? cm3.
V 36? 3 108? cm3
By tripling the radius, you would increase the
volume nine times.
23
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 4? 3
12? cm3.
V 4? 9 36? cm3
Tripling the height would triple the volume.
24
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
The volume of material needed to build the runway
was 1,584,000 ft3.
width 100 ft
height 2 ft
V 7920 100 2 ft3
1,584,000 ft3
25
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
27 ft3 1 yd3
26
Additional Example 4 Finding the Volume of
Composite Figures
Find the volume of the the barn.
30,000 10,000
40,000 ft3
The volume is 40,000 ft3.
27
Try This Example 4
Find the volume of the figure.
5 ft
96 60
4 ft
V 156 ft3
8 ft
3 ft
28
Lesson Quiz
Find the volume of each figure to the nearest
tenth. Use 3.14 for p.
10 in.
2 in.
1.
3.
2.
12 in.
12 in.
10.7 in.
15 in.
3 in.
8.5 in.
942 in3
306 in3
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.