Name: ____________________________________________ Period _____ Date __________________
UNIT 9:
Volume and Surface Area
Objectives:
 Calculate the volume of a rectangular prism or cube.
 Determine possible dimensions (length, width or height) of a cube or prism
when given the volume.
 Calculate the surface area of the lateral faces of a prism or cube.
 Calculate the total surface area of a prism or cube.
Vocabulary:
 Perimeter
Total distance around a shape
 Volume
The 3-dimensional space occupied by a solid
 Surface Area
The sum of the area of the faces of a 3-dimensional
Shape.
 Lateral faces
The face of a prism
that is not a base.
 Rectangular prism
A 3-dimensional figure with 2 parallel, congruent
faces called bases.
 Cube
A rectangular prism where all 3 dimensions
(length, width, and height) are the same.
Activity:
Open Agile Mind Lesson 9-1: Volume & Surface Area
1) Read the Overview pages 1, 2, 3, 4, & 5.
Calculating surface area and volume is useful in everyday life. List some examples of
ways that volume and surface area are used in everyday life. Some uses were
mentioned in the Overview.
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2) Explore pages 1 and 2 of the Understanding Volume section in Agile Mind.
Play the animation on page 2. View panels 1-6 and stop at panel 7.
Why do you think volume is measured in “cubic” units?
On panel 7 of the animation, try to determine the volume of the following prisms on your
own before playing this panel. Remember, each cube is 1cm x 1cm x 1cm.
Check your answers. How did you do?
3) View Page 4 of Understanding Volume.
Practice finding the area of the base of a prism by multiplying the length and width.
B=l•w
Next, set the height of the prism and calculate the volume. V = Bh or V = l • w • h
Practice: Calculate the volume of prisms with the following dimensions:
a) l = 5 w = 3 h = 4
______________ cubic units
b) l = 4 w = 4 h = 2
______________ cubic units
c) l = 3 w = 3
______________ cubic units
h=3
4) View Page 5 and try to answer the question.
Sean thinks 96 cubes may be too many for one package. He asks Kyle to make a
package that holds exactly 48 number cubes.
Can you help Kyle design a package that holds 48 number cubes?
When you are finished, check your answer in Agile Mind.
5) View Pages 6 & 7. For any prism, as long as you can
find the area of the base, you can multiply that value by the
height to find the volume. You know how to find the area of a
square and a rectangle. Can you use that information to
write a formula for the volume of each prism shown?
Match each formula with the shape whose volume it best
describes.
6) View Page 8. Fill in the blanks to find the volume of each prism. Use the answer
choices provided.
PRACTICE QUESTIONS: Complete the 4 “More Practice” questions at the end of the
lesson.
Practice Questions: Lesson 9-1 Volume & Surface Area
1) Business at Cheryl's Pak-It-Up is booming. It's doing so well, in
fact, that she is ready to move to a new location. She rents a truck to
move her things. The storage area of the truck is 10 feet long and 6
feet high. If it can hold 360 cubic feet, how wide is the storage area of
the truck?
2) Cheryl buys some storage boxes that are 2 feet long, 2 feet wide, and 2 feet high. How many storage
boxes can she fit in the back of the truck?
3) Cheryl packs 20 more boxes and takes them outside to wait
for the truck to return. It begins to rain and Cheryl needs a shelter
for the 20 boxes. Attached to the building is a tarp that forms the
shape of a rectangular prism with the dimensions shown. Is the
following statement true or false? The space under the tarp has
enough volume to hold the volume of the 20 boxes.
__________________
4) Cheryl has many items to pack, including her footstool. Her footstool is in the shape of a cylinder. It is
2 feet in diameter and 2.5 feet tall. The footstool just fits inside this storage
box.
The dimensions of the box are _______ft by______ft by _______ft.
The volume of the storage box is ______________ ft3.