1. Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes

2. Find the area of each figure. Use 3.14 for .
Warm Up
Find the area of each figure. Use 3.14 for .
1. rectangle with base length 8 in. and height 12 in.
96 in2
2. circle with diameter 8 ft
50.24 ft2 2

3. Volume of Prisms Problem of the Day
A rectangular park is bordered by a 3- foot-wide sidewalk. The park, including the sidewalk, measures 125 ft by 180 ft. What is the area of the park, not including the sidewalk?
20,706 ft2 3

4. Sunshine State Standards
MA.6.G.4.3 Determine the missing dimension of a prism…given its volume…or the volume given the dimensions.
Also MA.6.A.3.4

5. Vocabulary
volume 5

6. Volume is the number of cubic units needed to fill a space.6

7. You need 10, or 5 · 2, centimeter cubes to cover the bottom layer of this rectangular prism.
You need 3 layers of 10 cubes each to fill the prism. It takes 30, or 5 · 2 · 3, cubes.
Volume is expressed in cubic units, so the volume of the prism is 5 cm · 2 cm · 3 cm = 30 cm3. 7

8. Additional Example 1: Finding the Volume of a Rectangular Prism
Find the volume of the rectangular prism.
V = lwh
Write the formula.
V = 26 • 11 • 13
l = 26; w = 11; h = 13
V = 3,718 in3
Multiply. 8

9. Find the volume of each rectangular prism.
Check It Out: Example 1A
Find the volume of each rectangular prism.
V = lwh
= 2 × 3 × 8
= 48 ft 3 9

10. Find the volume of each rectangular prism.
Check It Out: Example 1B
Find the volume of each rectangular prism.
V = lwh
= 1 × 1 × 2
= 2 km 3

11. Find the volume of each rectangular prism.
Check It Out: Example 1C
Find the volume of each rectangular prism.
V = lwh
= 8.4 × 5.1 × 6
= in 3

12. To find the volume of any prism, you can use the formula V= Bh, where B is the area of the base, and h is the prism’s height. 12

13. Additional Example 2: Finding the Volume of a Triangular Prism
Find the volume of the triangular prism.
V = Bh
Write the formula.
V = ( • 3.9 • 1.3) • 4 1 2 __
B = • 3.9 • 1.3; h = 4. 1 2 __
V = m3
Multiply. 13

14. The bases of a prism are always two congruent, parallel polygons.
Caution! 14

15. Check It Out: Example 2A
V = Bh
(8)(7)12
= 336 ft 2 3 = 1 15

16. Check It Out: Example 2B V = Bh = ( )(2)1 1 1 3 2 2 4 7 m = 8 3 1 m 2
= ( )(2)1 2 1 2 1 4 3 8 7 m 3 = 1 m 2 16

17. Check It Out: Example 2C
V = Bh
= (3)(5.4)8.6 2 1 3
= 69.66 cm

18. Understand the Problem
Additional Example 3: Problem Solving Application
Suppose a facial tissue company ships 16 cubic tissue boxes in each case. What are the possible dimensions for a case of tissue boxes? 1
Understand the Problem
The answer will be all possible dimensions for a case of 16 cubic boxes.
List the important information:
There are 16 tissue boxes in a case.
The boxes are cubic, or square prisms. 18

19. Additional Example 3 Continued2
Make a Plan
You can make models using cubes to find the possible dimensions for a case of 16 tissue boxes. 19

20. Additional Example 3 Continued
Solve 3
You can make models using cubes to find the possible dimensions for a case of 16 cubes.
The possible dimensions for a case of 16 cubic tissue boxes are the following: 16 x 1 x 1, 8 x 2 x 1, 4 x 4 x 1, and 4 x 2 x 2. 20

21. Additional Example 3 Continued4
Look Back
Notice that each dimension is a factor of 16. Also, the product of the dimensions (length • width • height) is 16, showing that the volume of each case is 16 cubes. 21

22. Check It Out: Example 3
A toy box is a rectangular prism that is 3 ft long, 2 feet wide, and 2 feet tall. Another toy box has the same dimensions, except that it is longer. If the longer toy box has a volume that is 50% greater than the original toy box, what is the length of the longer toy box?
The original volume is 3 × 2 × 2 = 12 ft . 50% of 12 is 6, so the longer toy box has a volume of = 18 ft . So L × 2 × 2 = 18, and L = 18 ÷ 4 = 4.5. The length of the longer toy box is 4.5 feet. 3 22

23. Lesson Quiz for Student Response Systems
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems 23

24. Find the volume of each figure.
Lesson Quiz
Find the volume of each figure.
1. rectangular prism with length 20 cm, width 15 cm, and height 12 cm
2. triangular prism with a height of 12 cm and a triangular base with base length 7.3 cm and height 3.5 cm
3. Find the volume of the figure shown.
3,600 cm3
153.3 cm3
38.13 cm3 24

25. Lesson Quiz for Student Response Systems
1. Identify the volume of a rectangular prism with length 25 cm, width 20 cm, and height 10 cm.
A. 5,000 cm3
B. 5,225 cm3
C. 5,450 cm3
D. 5,650 cm3 25

26. Lesson Quiz for Student Response Systems
2. Identify the volume of a triangular prism with a height of 14 cm and a triangular base with base length 9.4 cm and height 4.5 cm.
A cm3
B cm3
C cm3
D cm3 26

27. Lesson Quiz for Student Response Systems
3. Identify the volume of the figure shown.
A cm3
B cm3
C cm3
D cm3 27