Unit 5 Review

Unit 5 Test Review

1. Describe the similarities and differences between a pyramid and a prism. Then draw a rectangular prism and a triangular pyramid.

Unit 5 Test Review

1. Describe the similarities and differences between a pyramid and a prism. Then draw a rectangular prism and a triangular pyramid.

Pyramid - Faces are triangles Has 1 base Faces meet at an Apex

Prism - Faces are rectangles Has 2 congruent bases

Unit 5 Test Review

1. Describe the similarities and differences between a pyramid and a prism. Then draw a rectangular prism and a triangular pyramid.

Pyramid - Faces are triangles Has 1 base Faces meet at an Apex

Prism - Faces are rectangles Has 2 congruent bases

Unit 5 Test Review

2. Mary, a college student, needs to walk from her dorm room in Wilson Hall to her math class in Wells Hall. Normally, she walks 500 meters east and 600 meters north along the sidewalks, but today she is running late. She decides to take the shortcut through the Tundra. a. How many meters long is Mary’s shortcut? b. How much shorter is the shortcut than Mary’s usual route?

Unit 5 Test Review

2. Mary, a college student, needs to walk from her dorm room in Wilson Hall to her math class in Wells Hall. Normally, she walks 500 meters east and 600 meters north along the sidewalks, but today she is running late. She decides to take the shortcut through the Tundra. a. How many meters long is Mary’s shortcut? b. How much shorter is the shortcut than Mary’s usual route?

5002 + 6002 = c2 250000 + 360000 = c2

610000 = c2 √610000 = c2

781 m ≈ c

500 + 600 = 1100 meters 1100 - 781 = 319 meters

Unit 5 Test Review

3. Name the space-shape that you could make from each of the following nets?

Unit 5 Test Review

3. Name the space-shape that you could make from each of the following nets?

rectangular prism

Square pyramid

tetrahedron

Unit 5 Test Review

4. Here are three views of a cube model. Draw the model.

How tall is the unit? How do you know?

Where is the tallest part of the cube model?

Top View Front View Right Side View

Unit 5 Test Review

4. Here are three views of a cube model. Draw the model.

How tall is the unit? How do you know? 3 units.

Where is the tallest part of the cube model? in the back

Unit 5 Test Review

5. Find all the symmetries of each of the following figures. Is there reflection symmetries (and where) and/or rotational symmetry (at what degree)?

Unit 5 Test Review5. Reflectional Symmetry

none none

none none none

4

2 4

2 2

Unit 5 Test Review5. Rotational Symmetry

90º, 180º, 270º 180º 180º

180º

90º, 180º, 270º 90º, 180º, 270º

90º, 180º, 270º 90º, 180º, 270º 90º, 180º, 270º 90º, 180º, 270º

Unit 5 Test Review

6. Tom has a room that he wants to paint all the walls in the room slate-gray. His room is 10 feet wide, 12 feet long and 8 feet high. How many square feet must he paint to paint the four walls (ignoring the less than needed paint for doors and windows! - pretend they don’t exist!)

If he wanted to fill the room to capacity at the end of painting, what is the cubic feet space that he has to fill?

Unit 5 Test Review

6. Tom has a room that he wants to paint all the walls in the room slate-gray. His room is 10 feet wide, 12 feet long and 8 feet high. How many square feet must he paint to paint the four walls (ignoring the less than needed paint for doors and windows! - pretend they don’t exist!)

If he wanted to fill the room to capacity at the end of painting, what is the cubic feet space that he has to fill?

352 feet2

960 ft3

Unit 5 Test Review

7. A can of vegetables has a base diameter of 6.5 cm and height of 9 cm. What is the surface area of the entire can? What is the lateral surface area of the label, and what is the volume of the can?

Unit 5 Test Review

7. A can of vegetables has a base diameter of 6.5 cm and height of 9 cm. What is the surface area of the entire can? What is the lateral surface area of the label, and what is the volume of the can?

SABases = 3.252π (base) = 10.56π ≈ 33.17 cm2 * 2 ≈ 66.33 cm2

SALA = 6.5π * 9 (lateral) ≈ 183.69 cm2

Total = 66.33 + 183.69 = 250.02 cm2

Unit 5 Test Review

7. A can of vegetables has a base diameter of 6.5 cm and height of 9 cm. What is the surface area of the entire can? What is the lateral surface area of the label, and what is the volume of the can?

SALA = 6.5π * 9 (lateral) ≈ 183.69 cm2

Unit 5 Test Review

7. A can of vegetables has a base diameter of 6.5 cm and height of 9 cm. What is the surface area of the entire can? What is the lateral surface area of the label, and what is the volume of the can?

V = 3.252π (base) 10.56π ≈ 33.17 cm2

*

9 ≈ 298.53 cm3 total

Unit 5 Test Review

8. A can of vegetables has a base diameter of 5 cm and height of 7 cm. What is the surface area of the entire can? What is the lateral surface area of the label, and what is the volume of the can?

Unit 5 Test Review

8. A can of vegetables has a base diameter of 5 cm and height of 7 cm. What is the surface area of the entire can? What is the lateral surface area of the label, and what is the volume of the can?

SA = 2.52π (base) 6.25π ≈ 19.625 cm2 * 2 ≈ 39.25 cm2

+ 5π * 7 (lateral) ≈ 109.9 cm2

Total = 149.15 cm2

Unit 5 Test Review

8. A can of vegetables has a base diameter of 5 cm and height of 7 cm. What is the surface area of the entire can? What is the lateral surface area of the label, and what is the volume of the can?

5π * 7 (lateral) ≈ 109.9 cm2

Unit 5 Test Review

8. A can of vegetables has a base diameter of 5 cm and height of 7 cm. What is the surface area of the entire can? What is the lateral surface area of the label, and what is the volume of the can?

V = 2.52π (base) .25π ≈ 19.625 cm22

*

7 ≈ 137.38 cm3 total

Unit 5 Test Review

9. A can of vegetables has a base diameter of 8 cm and height of 10 cm. What is the surface area of the entire can? What is the lateral surface area of the label, and what is the volume of the can?

Unit 5 Test Review

9. A can of vegetables has a base diameter of 8 cm and height of 10 cm. What is the surface area of the entire can? What is the lateral surface area of the label, and what is the volume of the can?

SA = 42π (base) 16π ≈ 50.24 cm2 * 2 ≈ 100.48 cm2

+ 8π * 10 (lateral) ≈ 251.2 cm2

Total = 351.68 cm2

Unit 5 Test Review

9. A can of vegetables has a base diameter of 8 cm and height of 10 cm. What is the surface area of the entire can? What is the lateral surface area of the label, and what is the volume of the can?

8π * 10 (lateral) ≈ 251.2 cm2

Unit 5 Test Review

9. A can of vegetables has a base diameter of 8 cm and height of 10 cm. What is the surface area of the entire can? What is the lateral surface area of the label, and what is the volume of the can?

V = 42π (base) 16π ≈ 50.24 cm2 *

10 ≈ 502.4 cm3 total