Name

Class

Date

9-1 • Guided Problem Solving GPS

  Student Page 299, Exercise 14–16:

Use the rectangular pyramid at the right. State whether each pair of line segments is intersecting, parallel, or skew. 14. CO,CE

15. OR,CE

O

16. CT , ER T

Understand

R

C

E All rights reserved.

1. What figure is formed by the line segments?  2. What are intersecting lines?

 3. What are parallel lines?

  4. What are skew lines?



© Pearson Education, Inc., publishing as Pearson Prentice Hall.



Plan and Carry Out 5. Trace CO and CE on the rectangular pyramid. O

6. If you extended these two line segments what would happen to them? 7. Therefore, these line segments are 8. Repeat Steps 5–7 for segments OR and CE and for segments

T

R

C

E

CT and ER .

Check 9. If CE and TR are parallel, what must then be true about the relationship between OT and TR ? 

Solve Another Problem 10. In the rectangular pyramid at the right, state whether line segments MN and PQ are intersecting, parallel, or skew. 

Q

N

R

P

M

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Course 3 Lesson 9-1

Guided Problem Solving

10/10/12 4:43 PM

Name

Class

Date

9-2 • Guided Problem Solving GPS

  Student Page 305, Exercise 20:

A store keeps roughly 240 boxes of crayons in its inventory. a. If each box measures 6 in. by 2.5 in. by 4 in., how many cubic inches of storage space does the store need for the crayons? b. One cubic foot is equal to (12 in.)3, or 1,728 in.3. Find the number of cubic feet necessary for storing 240 boxes of crayons. All rights reserved.

Understand 1. Circle the measures of the crayon boxes. 2. Underline how many boxes the art supply store has for inventory.

Plan and Carry Out 3. What formula will you use to find the volume of one box of crayons?

4. What is the volume of one box of crayons? 

 5. What operation will you use to find the volume of 240 boxes?

6. What is the volume of 240 boxes of crayons?



 © Pearson Education, Inc., publishing as Pearson Prentice Hall.

7. How many cubic inches are in one cubic foot?  8. How can you change cubic inches to cubic feet?  9. How many cubic feet are necessary for storing 240 boxes of crayons? 

Check 10. What is a way to check the problem?  

Solve Another Problem 11. A video store keeps approximately 350 boxes of storage cases in its inventory. a. If each storage case measures 1 in. by 5.5 in. by 8.75 in., how many cubic inches of storage space does the store need for the boxes of storage cases?  b. Find the number of cubic feet necessary for storing 350 boxes of cases. 

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Course 3 Lesson 9-2

Guided Problem Solving

10/10/12 4:43 PM

Name

Class

Date

9-3 • Guided Problem Solving GPS

  Student Page 312, Exercise 17:

Algebra  The volume of a square pyramid is 15 ft3. Its base area is 27 ft2.  What is its height?

Understand 1. Underline the measurements of the square pyramid you are given. All rights reserved.

2. What are you asked to find? 

Plan and Carry Out 3. What is the formula for finding the volume of a square pyramid?  4. What measurements are you given?  5. Substitute what you know into the formula.

© Pearson Education, Inc., publishing as Pearson Prentice Hall.

 6. What variable are you solving for?  7. Solve.



Check 8. How can you check your answer?  

Solve Another Problem 9. The volume of a cone is 113.04 ft3. Its base area is 28.26 ft2. What is its height?  

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Course 3 Lesson 9-3

Guided Problem Solving

10/10/12 4:43 PM

Name

Class

Date

9-4 • Guided Problem Solving GPS

  Student Page 316, Exercise 16:

The circumference of a glass terrarium in the shape of a sphere is about 12.5 in. What is the surface area of the terrarium to the nearest square inch?

Understand 1. What is the given measurement? All rights reserved.

2. What formula do you use to find circumference?  3. What are you being asked to find? 

Plan and Carry Out 4. How can you use the circumference to find the surface area?   5. What is the radius of the terrarium? © Pearson Education, Inc., publishing as Pearson Prentice Hall.

 6. How will you find the surface area of the terrarium?

 7. What is the surface area of the terrarium to the nearest square inch?



Check 8. Does your answer check? Is your answer consistent with the circumference given in the question? 

Solve Another Problem 9. The volume of a weather balloon is about 33.5 ft3. What is the surface area of the weather balloon? Round your answer to the nearest whole square unit.  

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Course 3 Lesson 9-4

Guided Problem Solving

10/12/12 12:11 PM

Name

Class

Date

9-5 • Guided Problem Solving GPS

  Student Page 322, Exercise 14:

Carpentry  Gina used 78 square feet of plywood to build a storage bin to hold her gardening supplies. How much plywood will she need to build a similar box for her hand tools if the dimensions of the box are half the dimensions of the bin?

Understand All rights reserved.

1. What are you asked to do?   2. How many square feet of plywood did Gina use?

Plan and Carry Out 3. What is the ratio for the surface area of similar solids? 4. What are the dimensions of the similar box?   © Pearson Education, Inc., publishing as Pearson Prentice Hall.

5. What is the ratio of the surface areas?  6. Write a proportion.  7. Solve. 

Check 8. How can you tell if your answer is reasonable?   

Solve Another Problem 9. In pottery class, Mark made a small cylindrical bowl with a volume of 75 in.3 and a radius of 2 inches. He also made a larger bowl with a similar shape. It has a diameter of 8 inches. Find the volume of the larger bowl. 

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Course 3 Lesson 9-5

Guided Problem Solving

10/10/12 4:43 PM