Geometry Volume of Prisms and Cylinders

1
Geometry Volume of Prisms and Cylinders
2
Warm Up
1) Marcy, Rachel, and Tina went bowling. Marcy
bowled 100 less than twice Rachels score. Tina
bowled 40 more than Rachels score. Rachel bowled
a higher score than Marcy. What is the greatest
score that Tina could have bowled? 2) Max can
type 40 words per minute. He estimates that his
term paper contains about 5000 words, and he
takes a 15-minute break for every 45 minutes of
typing. About how much time will it take Max to
type his term paper?
3
Volume of Prisms and Cylinders
The volume of a three-dimensional figure is the
number of nonoverlapping unit cubes of a given
size that will exactly fill the interior.
Next Page
4
Cavalieri's principle says that if two
three-dimensional figure have the same height and
have the same cross-sectional area at every
level, they have the same volume.
5
Volume of a Prism
The volume of a prism with base area B and height
h is V Bh.
Next Page
6
(No Transcript)
7
Finding Volumes of Prisms
Find the volume of each prism. Round to the
nearest tenth, if necessary.
A).
volume of a right rectangular prism Substitute 10
for l, 12 for w, and 8 for h is V lwh.
Next Page
8
Next Page
9
C). A right regular pentagonal Prism with base
edge length 5 m and height 7 m.
Find the apothem a of the base . First draw a
right triangle on one base as shown. The measure
of the angle with its vertex at the center is
360/10 36
Step1
tan 36 2.5/a The leg of the triangle is
half the side
length. Or 2.5 m. a 2.5/tan 36 Solve for a.
Next Page
10
Use the value of a to find the base area.
Step2
Use the base area to find the volume.
Step3
11
Now you try!
1) Find the volume of a triangular prism with a
height of 9 yd whose base is a right triangle
with legs 7 yd and 5 yd long.
12
Marine Biology Application
Next Page
13
Find the volume of the aquarium in cubic feet.
Step1
Next Page
14
Step2
Next Page
15
Step3
The aquarium holds about 429,851 gallons. The
water in the aquarium weight about 3,580,659
pounds
16
Now you try!
2) Estimate the volume in gallons and the
weight of the water in the aquarium below if the
height were doubled.
17
Cavalieris principle also relates to cylinders.
The two stacks have the same number of CDs, so
they have the same volume.
18
(No Transcript)
19
Finding Volumes of Cylinders
A).
Next Page
20
Step1
Use the base area to find the radius.
Use the radius to find the height. The height is
equal to twice the radius.
Step2
Use the radius and height to find the volume.
Step3
21
Now you try!
22
Exploring Effects of Changing Dimensions
The radius and height of the cylinder are
multiplied by ½. Describe the effect on the
volume.
23
Now you try!
4) The length, width, and height of the prism
are doubled. Describe the effect on the
volume.
24
Finding Volumes of Composite Three-Dimensional
Figures
Find the volume of the composite figure. Round to
the nearest tenth.
25
Now you try!
5) Find the volume of the composite figure.
Round to the nearest tenth.
26
Now some problems for you to practice !
27
Assessment
1. Find the volume of each prism.
B)
A)
28
2. The worlds largest ice cream cake, built in
New York City on may 25, 2004, was approximately
a 19 ft by 9 ft by 2 ft rectangular prism.
Estimate the volume of the ice cream cake in
gallons. If the density of the ice cream cake was
4.73 pounds per gallon, estimate the weight of
the cake. (Hint 1 gallon 0.134 cubic feet)
29
B)
A)
30
4. Describe the effect of each change on the
volume of the given figure.
A) The dimensions are multiplied by ¼ .
B) The dimensions are tripled.
31
5. Find the volume of each composite figure.
Round to the nearest tenth.
B)
A)
15 in.
14 ft
32
Lets review
33
Volume of Prisms and Cylinders
The volume of a three-dimensional figure is the
number of nonoverlapping unit cubes of a given
size that will exactly fill the interior.
Next Page
34
Cavalieri's principle says that if two
three-dimensional figure have the same height and
have the same cross-sectional area at every
level, they have the same volume.
35
Volume of a Prism
The volume of a prism with base area B and height
h is V Bh.
Next Page
36
(No Transcript)
37
Finding Volumes of Prisms
Find the volume of each prism. Round to the
nearest tenth, if necessary.
A).
volume of a right rectangular prism Substitute 10
for l, 12 for w, and 8 for h is V lwh.
Next Page
38
Next Page
39
C). A right regular pentagonal Prism with base
edge length 5 m and height 7 m.
Find the apothem a of the base . First draw a
right triangle on one base as shown. The measure
of the angle with its vertex at the center is
360/10 36
Step1
tan 36 2.5/a The leg of the triangle is
half the side
length. Or 2.5 m. a 2.5/tan 36 Solve for a.
Next Page
40
Use the value of a to find the base area.
Step2
Use the base area to find the volume.
Step3
41
Marine Biology Application
Next Page
42
Find the volume of the aquarium in cubic feet.
Step1
Next Page
43
Step2
Next Page
44
Step3
The aquarium holds about 429,851 gallons. The
water in the aquarium weight about 3,580,659
pounds
45
Cavalieris principle also relates to cylinders.
The two stacks have the same number of CDs, so
they have the same volume.
46
(No Transcript)
47
Finding Volumes of Cylinders
A).
Next Page
48
Step1
Use the base area to find the radius.
Use the radius to find the height. The height is
equal to twice the radius.
Step2
Use the radius and height to find the volume.
Step3
49
Exploring Effects of Changing Dimensions
The radius and height of the cylinder are
multiplied by ½. Describe the effect on the
volume.
50
Finding Volumes of Composite Three-Dimensional
Figures
Find the volume of the composite figure. Round to
the nearest tenth.
51
You did a great job today!