Name:
Period
GL
UNIT 11: SOLIDS
I can define, identify and illustrate the following terms:
Isometric View
Face
Net
Polyhedron
Edge
Volume
Cylinder
Vertex
Hemisphere
Cone
Cross section
Height
Pyramid
Slant height
Prism
Lateral Face
Lateral Edge
Surface area
Lateral surface area
Oblique Prism
Altitude
Base
Sphere
Great Circle
Right Prism
Orthographic View
Dates, assignments, and quizzes subject to change without advance notice.
Monday
Tuesday
Block Day
Friday
8
Basics
SPRING BREAK
18
Prisms and Pyramids
25
Dimensional Changes
19
Cylinders, Cones, and
Spheres
20/21
Applications
26
27/28
Review
22
Composites
TEST
Friday, 3/8
Views and Faces: Chapter 10 sections 1 - 3
I can identify and draw orthographic and isometric views
I can identify the number of faces, edges, and vertices
I can identify the cross-sections of solid figures
I can match solids and nets
I can identify and draw orthographic and isometric views
PRACTICE: Solids View and Net Practice Worksheet
Monday, 3/18
Prisms and Pyramids: Chapter 10 sections 4 - 7
I can classify prisms and pyramids
I can find the surface areas and volume of solids
I can solve problems using surface areas and volume
PRACTICE: Prism and Pyramids Worksheet
Tuesday, 3/19
Cylinders, Cones, and Spheres: Chapter 10 sections 4 - 8
I can find the surface areas and volume of solids
I can solve problems using surface areas and volume
PRACTICE: Cylinders, Cones, and Spheres Worksheet
Block, 3/20-21
Applications
I can find the surface areas and volume of solids
I can solve problems using surface areas and volume
PRACTICE: Applications Worksheet
1
Friday, 3/22
Composites
I can find the surface areas and volume of composite solids
I can solve problems using surface areas and volume
PRACTICE: Composite Worksheet
Monday, 3/25
Dimensional Changes
I can determine the effect on surface areas and volume when one or more dimensions are changed
PRACTICE: Dimensional Changes Worksheet
Tuesday, 3/26
Review
I can assess my strengths and weaknesses on all previously learned material.
PRACTICE: Review Activity
Block day, 3/27-28
Test Unit #11: Solids
I can demonstrate my ability on all previously learned material.
2
Notes: Surface Area and Volume of Prisms and Pyramids
I. Vocabulary
There are two _______________ ________________of a solid. The ____________ surface area is the
amount of surface on the ____________ _____________of the solid. This does NOT include the
_____________. The _____________ surface area is the amount of surface on ___________ faces. The
_______________ of a solid is how much they can hold. It is measured in ___________ measurements.
II. Prisms
Formulas:
Lateral Surface area = _____________________
Total Surface Area = _____________________
Volume = _____________
The P stands for the _______________ of the _________. The B stands for the ___________ of the
_________ and the h stands for the _________. In other words you have to __________ for the P and
the B and the h is a _____________.
8.7 ft
Examples:
3 in
4 in
10 ft
15 in
31 ft
LSA = _________
LSA = _________
SA = _________
SA = _________
V = _________
V = _________
LSA = _________
3
2
SA = _________
V = _________
5
3
III. Pyramids
Formulas:
Lateral Surface area = _____________________
Total Surface Area = _____________________
Volume = _____________
The _________, h, of a regular Pyramid is the distance from the _________ to the ________ of the base.
The _________ _________, l, of a regular pyramid is the __________ of a lateral face.
Examples:
24 cm
26 cm
20 cm
20 cm
LSA = _________
LSA = _________
SA = _________
SA = _________
V = _________
V = _________
15 m (l)
LSA = _________
12 m (h)
SA = _________
V = _________
18 3 m
9 m (a)
4
Assignment – Prisms and Pyramids
For each solid, find the lateral surface area (LSA), total surface area (SA), and volume (V).
1. LSA = _________
2. LSA = _________
SA = __________
SA = __________
V = ___________
V = ___________
3. LSA = _________
4. LSA = _________
SA = __________
SA = __________
V = ___________
V = ___________
16 cm
5 cm
8 cm
12cm
5. LSA = _________
6. LSA = ________
13 cm
SA = __________
SA = __________
V = ___________
6m
V = ___________
10 cm
10 cm
2m
8m
25 m (l)
7. LSA = _________
SA = __________
8. LSA = _________
24 m (h)
V = ___________
7 m (a)
SA = __________
V = ___________
14 3 m
5
9. The base of a triangular prism is an equilateral triangle with a perimeter of 24 inches. If the height of
the prism is 5 inches, find the lateral area.
F) 120 in2
G) 60 in2
H) 40 in2
J) 360 in2
10) Find the surface area, lateral surface area and volume of a rectangular prism with height 7 m, length
10 m, and width 8 m.
11) What equation would be used to find the surface area for the pyramid?
1
(36)(4) + 2(36)
2
1
C) S = (24)(5) + 36
2
A) S =
1
(36)(5) + 2(36)
2
1
D) S = (24)(4) + 36
2
B) S =
26 m
7m
12) What equation would be used to find the lateral surface area of a right triangular prism?
(10)(24)
10 + 24
A) S = (10 + 24 + 26)(7) + 2(
)
B) S = (10 + 24 + 7)(26) + (
)
2
2
D) S = (10 + 24 + 26)(7) + 2(10)(24)
C) S = (24 + 24 + 7 + 7)(10) + 2(24)(7)
24 m
10 m
13) What equation would be used to find the volume for the pyramid with apothem of 5.5 cm, a side
length of 8 cm, and a height of 10 cm?
1 1
1  (5.5)(40) 
A) V = ( )(5.5)(8)(10)
B) V = 
 (10)
3 2
3
2

1
1  (5.5)(8) 
D) V = (5.5)(8)(10)
C) V = 
 (10)
3
3 2 
14) What is the area of this triangle, to the nearest square inch?
A) 22 in2
B) 38 in2
C) 43 in2
D) 75 in2
15) The hypotenuse of a right triangle is 89 units. One leg is 39 units. What is the length of the other
leg?
A) 50 units
B) 62 units
C) 80 units
D) 97 units
6
Cylinders - Notes
Cylinders
Prisms
Cylinder Formulas: LSA = _________________, SA = _________________, V = ________
15 m
LSA = _________
What is height of cylinder? ______
SA = __________
What is radius of cylinder? _______
43 m
V = ___________
What does B stand for? ____________
YOU TRY:
LSA = _________
12 cm
8 cm
SA = __________
V = ___________
Spheres - Notes
Sphere Formulas: Surface Area = _________________, Volume = _________________
SA = __________
SA = __________
V = ___________
V = ___________
YOU TRY:
SA = __________
SA = __________
V = ___________
V = ___________
7
Cones - Notes
Cylinders
Cones
Cone Formulas: LSA = ___________________, SA = __________________, V = ___________
LSA = _________
What is the height of the cone? ________
SA = __________
What is the radius of the base? _________
V = ___________
What is the slant height of the cone? _______
YOU TRY:
4m
LSA = _________
SA = __________
16 m
V = ___________
8
Cylinders, Cones, and Spheres Worksheet
1. LSA = _________
2. LSA = _________
SA = __________
SA = __________
V = ___________
V = ___________
3. LSA = _________
4. LSA = _________
SA = __________
SA = __________
V = ___________
V = ___________
5. LSA = _________
SA = __________
6. SA = __________
V = ___________
V = ___________
7. SA = __________
8. SA = __________
V = ___________
V = ___________
9. Find the diameter of a cone with slant
height 18 and lateral surface area 162π.
10. Susan has a fish tank in the shape of a
cylinder that is 26 inches tall. The diameter of
the tank is 12 inches. If there are 2 inches of
rocks in the bottom, how much water is needed
to fill the tank?
11.
9
12. For small paving jobs, a contractor uses a roller pushed by a worker. What is the area of pavement
with which the surface of the roller will come into contact in one complete rotation?
13.
14.
15.
10
Notes – Applications of Solid Figures
1. Find the height of a cylinder with a surface area of 160π ft2 and radius of 5 ft.
2. Abigail has a cylindrical candle mold with the dimensions shown. If Abigail has a rectangular block
of wax measuring 15 cm by 12 cm by 18 cm, about how many candles can she make after melting the
block of wax?
A) 14
B) 31
C) 35
D) 76
3. Michael is refinishing the bookcase pictured to the left. How much area will he cover
if he only paints the left side, right side, and back of the book case with two coats?
4 ft
6 ft
6 in.
4. The Imaginary Toy Company, has increased their size of the “Creativity Doll”. The packaging
department has calculated that they need to add 3 inches to each of the dimension of the original
packaging (Original is shown in Picture). What is the new amount of cardboard needed to package one
doll?
10 in
5.
5 in
3 in
11
Practice and Applications
1. The greater the lateral area of a florescent light bulb, the more light the bulb produces. One
cylindrical light bulb is 16 inches long with a 1 inch radius. Another is 23 inches long with a ¾
inch radius. Which bulb produces more light?
2. The base of a triangular prism is an equilateral triangle with a perimeter of 24 inches. If the
height of the prism is 5 inches, find the lateral area.
F) 120 in2
G) 60 in2
H) 40 in2
J) 360 in2
3. A juice container is a square prism with base edge length 4 in. When an 8 in. straw is inserted
into the container as shown, exactly 1 in. remains outside the container.
a) How much of the straw is in the container?
b) Find BC
c) Use BC and the straw to find AC
d) Now use the height (answer to part c) to find how much material is required to manufacture
the container. Round to the nearest tenth.
4.
5. Which of the following equations would answer the problem below?
Susan has a fish tank in the shape of a cylinder that is 26 inches tall. The diameter of the tank is
12 inches. If there are 2 inches of rocks in the bottom, how much water is needed to fill the tank?
A) V = π (12) 2 (26)
B) V = π (6)2 (26)
C) V = π (12) 2 (24)
D) V = π (6)2 (24)
12
6.
7. If one gallon of paint covers 250 square feet, how many gallons of paint will be needed to cover
the shed, not including the roof? If a gallon of paint costs $25, about how much will it cost to
paint the walls of the shed?
8. Colin is buying dirt to fill a garden bed that is a 9 ft by 16 ft rectangle. If he wants to fill it to a
depth of 4 in., how many cubic yards of dirt does he need? If dirt costs $25 per yd3, how much
will the project cost? (Hint: 1 yd3 = 27 ft3)
9. The base of a triangular prism is an equilateral triangle with a perimeter of 24 inches. If the
height of the prism is 5 inches, find the lateral area.
F) 120 in2
G) 60 in2
H) 40 in2
J) 360 in2
7.
8.
13
10. A right circular cylinder has a volume of 1,000 cubic inches and a height of 8 inches. What is the
radius of the cylinder to the nearest tenth of an inch?
A) 6.3 in
B) 11.2 in
C) 19.8 in
D) 39.8 in
11.
12.
13.
14.
15.
16.
14
17.
18.
19.
20.
15
Prisms and Pyramid: Composite and Nets Notes and Assignment
A composite figure is made up of _____________ or more geometric figures combined.
**Keep in mind that some of the sides may not be in the surface area if they are now part of the interior of the figure.
Polyhedron – a ___________ figure with __________ surfaces
Example 1
Example 2
LSA = _________
SA = __________
SA = __________
V = ___________
V = ___________
Faces - ______
Edges - ______
Vertices - ______
4 in
Example 3 & 4:
LSA = _________
SA = __________
V = ___________
5. V = ___________
LSA = _________
8 in
SA = __________
V = ___________
10 in
6. SA = ___________
16
7. If one gallon of paint covers 250 square feet, how many gallons of paint will be needed to cover the
shed, not including the roof? If a gallon of paint costs $25, about how much will it cost to paint the walls
of the shed?
8. Find the height of a rectangular prism with length 5 ft, width 9 ft, and volume 495 ft3.
9. Colin is buying dirt to fill a garden bed that is a 9 ft by 16 ft rectangle. If he wants to fill it to a depth
of 4 in., how many cubic yards of dirt does he need? If dirt costs $25 per yd3, how much will the project
cost? (Hint: 1 yd3 = 27 ft3)
10. You can use displacement to find the volume of an irregular object, such as a stone. Suppose the
tank shown is filled with water to a depth of 8 in. A stone is placed in the tank so that it is completely
covered, causing the water level to rise by 2 in. Find the volume of the stone.
11. V = _____________________
SA = ____________________
12. V = _____________________
SA = ____________________
17
13.
V = _____________________
SA = ____________________
Which of the following equations can NOT be used to find the volume?
A) V = π (22)(4) + (12)(4)(4)
B) V = 16π + (192)
C) V = ½ [π (22)(4)] + (12)(4)(4)
D) V = 4π (4) + (12)(4)(4)
The answer is _______. The others don’t work because….
_____________________________________________________________________
_____________________________________________________________________
____________________________________________________________________.
14. Abigail has a cylindrical candle mold with the dimensions shown. If Abigail has a rectangular block
of wax measuring 15 cm by 12 cm by 18 cm, about how many candles can she make after melting the
block of wax?
A) 14
B) 31
C) 35
D) 76
15. The answer is _______. The others don’t work because….
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
____________________________________
____________________________________
____________________________________
____________________________________
____________________________________
________________________________.
18
16. The answer is _______. The others don’t
work because….
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
_________________________________.
17.
The answer is _______. The others don’t work because….
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
________________________________________.
18.
Describe the steps needed to solve this problem:
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
______________________________________________________________________.
19
Dimensional Changes in Volume
Review:
What will happen to the PERIMETER of a similar figure when you multiply
the dimensions by any scale factor?
What happens to the AREA of a similar figure when you change the
dimensions by a scale factor?
Extend to Volume:
A. Find the volume of a 1 x 2 x 3 rectangular prism. The volume is ________.
Now find the volume for a similar rectangular prism whose dimensions are
double the dimensions of the first prism. The new volume is ___________.
When you double the dimensions of a rectangular prism, the volume is
___________ times the volume of the original prism.
B. Find the volume of a cube with an edge of 4 units. The volume is
________.
Now find the volume for a similar cube whose dimensions are half the
dimensions of the first prism. The new volume is ___________.
When you half the dimensions of a figure, the volume is ___________ times
the volume of the original figure.
Original
Scale factor
A
B
Volume
Scale factor
Conclusion: What happens to
the VOLUME of a similar solid
when you change the
dimensions by a scale factor?
20
Examples:
1.
2.
2006 Exit Modified
3. Campbell’s manufactures a cylindrical soup can that has a diameter of 6 inches and a volume of 226
in3. If the stays height the same and the diameter is doubled, what will happen to the can’s volume?
A
B
C
D
It will remain the same.
It will double.
It will triple.
It will quadruple.
4. If the volume of a cube is increased by a factor of 8, what is the change in the length of the sides of
the cube?
5. Describe the change to the surface area and volume of the cylinders.
Why is the following not a dimensional change problem?
6. The radius of a spherical beach ball is 24 centimeters. If another spherical beach ball has a radius 3
centimeters longer, about how much greater is its volume, to the nearest cubic centimeter?
21
Dimensional Changes Worksheet
1
1. If the volume of a cube is increased by a factor of , what is the change in the length of the sides of
8
the cube?
2. A rectangular solid has a volume of 24 cubic decimeters. If the length, width, and height are all
changed to
A
1
their original size, what will be the new volume of the rectangular solid?
2
3 dm3
B 4 dm3
C 6 dm3
D 12 dm3
3. Bri’asia was inflating a soccer ball. She measured the radius initially to be 6 inches. What
effect would inflating the ball to 12 inches have on the volume of the air inside the soccer ball?
What is the ratio of the volume of the ball with less air to when it has more air?
4. A sphere has a diameter of 5 feet. If it is expanded to 2.5 times its diameter, what will be its change in
volume?
5.
7.
6.
Brendan and Rachel both had a rectangle in front of them. If Brendan’s rectangle was
2
of Rachel’s
3
rectangle, what is the ratio of area of Brendan’s rectangle to Rachel’s?
2
4
4
8
[A]
[B]
[C]
[D]
[E] None of these
3
6
9
27
8. The We-R-Tubes company has 2 similar but differently sized cylindrical tubes. The larger tube holds
125 cm3 while the smaller tube can only hold 27 cm3. Which statement correctly describes how a
person could find the ratio of the areas of each circle of the cylinder?
[A] Take the cube root of each volume to find the ratio of the areas.
[B] Take the cube root of each volume then double it to find the ratio of the areas.
[C] The ratio of the volume of the cylinders is equal to the ratio of the area of the circles.
[D] Take the cube root of each volume then square it to find the ratio of the areas.
22
9.
10.
.
11.
12. Describe the effect on the volume and surface
area for the given figure.
13. Describe the effect on the volume and surface
area for the given figure.
14. Describe the effect on the volume and surface
area for the given figure.
15. A rectangular garden is 20 feet long and 30 feet wide. The owner decided to increase the garden by
doubling the length but leaving the width the same. Which statement correctly describes what happened
to the area of the garden?
[A] The area of the garden stayed the same.
[B] The area of the garden doubled.
[C] The area of the garden tripled.
[D] The area of the garden quadrupled.
[E] The area can not be determined since only one side increased.
23
REVIEW
1) The drawing shows the top view of a structure built with cubes as well as the
number of cubes in each column of the structure.
Which 3-dimensional view represents the same structure?
F
G
H
J
2) How many faces, edges, and vertices are in each figure?
Faces: _______
Faces: ________
Edges: _______
Edges: ________
Vertices: ______
Vertices: ______
3) Match the nets with their corresponding solid.
A.
B.
_______
C.
_________
D.
_______
E.
_______
_______
24
#4-9: Find the lateral surface area, total surface area, and volume. ROUND ALL ANSWERS TO
THE NEAREST TENTH.
4)
5)
5 in
12 cm
2 in
14 in.
4 cm
*Shaded part is the base
*Use 3.14 for Pi
P =________
P =________
B=_________ h=_______
LSA = ________ SA = ________ V = ________
________
6)
5 in
3 in
B=_________ h=_______
LSA = ________ SA = ________V =
7) Regular hexagonal prism with apothem of 2 3
7 mm
10 in
4 mm
P =________
B=_________ h=_______
LSA = ________ SA = ________ V = ________
________
P =________
B=_________ h=_______
LSA = ________ SA = ________V =
25
8)
16 in
20 in
9)
24 in
LSA = ________ SA = ________ V = ________
________
LSA = ________ SA = ________ V =
10) Given the following rectangular prism, answer the following questions about a similar prism in
which the dimensions have been tripled.
4 ft
5 ft
12 ft
a) What are the new dimensions? ___________, _____________, _____________
b) What is the new volume? V=______________
c) The volume of the new prism is _____ times larger than the volume of the original prism.
11) Disney wants to make a new version of Arial that is larger than the original. They now need to
increase the dimensions of the old box by a factor of 2.5. If the old surface area was 838 in2 and the
old volume was 1463 in3, to the nearest tenth what will be surface area and volume for the new box?
12) If the surface area of a cube is increased by a factor of 16, what is the change in the length of the
sides of the cube?
26
13) A cube-shaped piece of playground equipment has a cylindrical portion removed, as shown in the
diagram. The diameter of the opening is 5 feet.
What is the approximate volume of
the remaining portion of the cube?
6 ft
6 ft
6 ft
14) Write an equation to find the volume of the composite figure. Use the numbers in the given figure.
15) A company packages their product in two sizes of cylinders. Each dimension of the larger cylinder is
three times the size of the corresponding dimension of the small cylinder. Based on this information,
how much bigger is the larger cylinder’s volume from the smaller cylinder’s volume?
3r
r
h
3h
16) What is the best description of the solid figure shown?
A
B
C
D
a regular polygon
a convex polygon
a regular polyhedron
a nonregular polyhedron
4
4
4
27