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Name: ___________________________________________ Period: ____ Chapter 14: Surface Area & Volume

Part 1: Directions: For each shape:

Name it

Draw the net

Count & record the number of faces, edges & vertices

1. Shape: Triangular Prism

Faces = 5

Edges = 9

Vertices = 6

2. Shape: _______________________________

Faces =

Edges =

Vertices =

3. Shape: __________________________________

Faces =

Edges =

Vertices =

4. Shape: __________________________

Faces =

Edges =

Vertices =

2

5. Shape: ________________________

Faces =

Edges =

Vertices =

6. Shape: _________________________

Faces =

Edges =

Vertices =

Part 2:

Write the dimensions on each of the parts & find the area of each part. Use the net to calculate the surface area

of the figure. (Note: all measurements are in centimeters.)

1) . 2)

3) . 4)

3

5)

Draw a net for each prism. Write the dimensions for each shape of the net. Then find the

surface area & volume of each figure to the nearest whole unit.

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11

11.

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For the four nets below. All of them fold into rectangular boxes. Net iii folds into an open

box. The other nets fold into closed boxes. Answer the 3 questions for each net.

a. What are the dimensions of the box that can be made from the net?

b. What is the surface area of the box?

c. What is the volume for each shape?

a) Dimensions: ______________________________________

b) Surface Area: ____________________________________

c) Volume: __________________________________________

a) Dimensions: ______________________________________

b) Surface Area: ____________________________________

c) Volume: __________________________________________

a) Dimensions: ______________________________________

b) Surface Area: ____________________________________

c) Volume: __________________________________________

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a) Dimensions: ______________________________________

b) Surface Area: ____________________________________

c) Volume: __________________________________________

2a. Gina has a sheet of cardboard that measures 9 feet by 6 feet. She uses scissors and

tape to make the entire sheet of cardboard into a closed box that is a perfect cube. What

is the surface area of the box? Draw the net and label the dimensions.

2b. How many unit cubes would it take to fill Gina’s box? Explain your reasoning.

3a. The rectangular prism at the left is made from centimeter

cubes. What are the dimensions of the prism?

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3b. What is the surface area of the prism?

3c. What is the volume of the prism? That is, how many cubes are in the prism?

3d. Give the dimensions of a different rectangular prism that can be made from the same

number of cubes. What is the surface area of the prism? Draw this rectangular prism.

4. Find the surface area and volume of each box.

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Name the 3-dimensional shape that will form from each net below.

6.

7. . 8. 9.

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Find the surface area of each figure to the nearest square unit.

7. Isosceles Triangular Prism 8. Right Triangular Prism

8. Square Pyramid 9. Rectangular Prism & Square Pyramid

5 m 4 m

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10. Find the surface area of the square pyramid net below.

Make a net of each figure & name each 3-dimensional figure.

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Lesson 11: Volume with Fractional Edge Lengths & Unit Cubes

Classwork

Opening Exercise

Which prism will hold more 1 in. × 1 in. × 1 in. cubes?

How many more cubes will the prism hold?

Example 1

A box with the same dimensions as the prism in the Opening Exercise will be used to ship miniature

dice whose side lengths have been cut in half. The dice are 1

2 in. ×

1

2 in. ×

1

2 in. cubes. How many dice

of this size can fit in the box?

6 in.

4 in.

10 in.

6 in.

4 in. 10 in.

5 in.

12 in.

8 in.

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Example 2

A 1

4 in. cube was used to pack the prism.

a) How many 1

4 in. cubes will it take to fill the prism?

b) What is the volume of the prism?

c) How is the number of cubes related to the volume?

Exercises 1–5

1. Use the prism to answer the following questions.

a. Calculate the volume.

b. If you have to fill the prism with cubes whose side lengths are less than 1 cm, what size would

be best?

c. How many of the cubes would fit in the prism?

d. Use the relationship between the number of cubes and the volume to prove that your volume

calculation is correct.

33

4 in.

1 in.

11

2 in.

𝟓𝟏

𝟑 𝐜𝐦

𝟐

𝟑𝐜𝐦

𝟏𝟏

𝟑𝐜𝐦

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2. Calculate the volume of the following rectangular prisms.

a.

b.

3. A toy company is packaging its toys to be shipped. Some of the very small toys are placed inside

a cube shaped box with side lengths of 1

2 in. These smaller boxes are then packed into a shipping

box with dimensions of 12 in. × 41

2 in. × 3

1

2 in.

a. How many small toys can be packed into the larger box for shipping?

b. Use the number of toys that can be shipped in the box to help determine the volume of the

box.

𝟐𝟑

𝟒 𝐜𝐦

𝟏

𝟐 𝐜𝐦

𝟏𝟏

𝟒 𝐜𝐦

𝟑𝟏

𝟑 𝐢𝐧.

𝟑𝟏

𝟑 𝐢𝐧.

𝟓𝟐

𝟑 𝐢𝐧.

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4. A rectangular prism with a volume of 8 cubic units is filled with cubes. First it is filled with cubes

with side lengths of 1

2 unit. Then it is filled with cubes with side lengths of

1

3 unit.

a. How many more of the cubes with 1

3 unit side lengths than cubes with

1

2 unit side lengths will be

needed to fill the prism?

b. Why does it take more cubes with 1

3 unit side lengths to fill the prism?

5. Calculate the volume of the rectangular prism. Show two different methods for determining the

volume.

41

2 m

3

4 m

11

2 m

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HOMEWORK Problem Set: Complete on a separate piece of paper.

1. Answer the following questions using this rectangular prism:

a. What is the volume of the prism?

b. Linda fills the rectangular prism with cubes that have side lengths of 1

3 in. How many cubes

does she need to fill the rectangular prism?

c. How is the number of cubes related to the volume?

d. Why is the number of cubes needed different than the volume?

e. Should Linda try to fill this rectangular prism with cubes that are 1

2 in. long on each side? Why

or why not?

2. Calculate the volume of the following prisms.

a.

b.

24 cm

41

2 cm

22

3 cm

𝟒𝟐

𝟑 𝐢𝐧.

𝟗 𝐢𝐧. 𝟏

𝟏

𝟑 𝐢𝐧.

23

4in.

𝑖𝑛

32

5in.

51

2 in.

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3. A rectangular prism with a volume of 12 cubic units is filled with cubes. First it is filled with cubes

with 1

2 unit side lengths. Then it is filled with cubes with

1

3 unit side lengths.

a. How many more of the cubes with 1

3 unit side lengths than cubes with

1

2 unit side lengths will be

needed to fill the prism?

b. Finally, the prism is filled with cubes whose side lengths are 1

4 unit. How many

1

4 unit cubes

would it take to fill the prism?

4. A toy company is packaging its toys to be shipped. Some of the toys are placed inside a cube

shaped box with side lengths of 31

2 in. These boxes are then packed into a shipping box with

dimensions of 14 in. × 7 in. × 31

2 in.

a. How many toys can be packed into the larger box for shipping?

b. Use the number of toys that can be shipped in the box to help determine the volume of the

box.

5. A rectangular prism has a volume of 34.224 cubic meters. The height of the box is 3.1 meters, and

the length is 2.4 meters.

a. Write an equation that relates the volume to the length, width, and height. Let 𝑤 represent

the width, in meters.

b. Solve the equation.