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

2. Warm Up Identify the figure described.
1. two triangular faces and the other faces in the shape of parallelograms
2. one hexagonal base and the other faces in the shape of triangles
3. one circular base and a curved lateral surface that forms a vertex
triangular prism
hexagonal pyramid
cone

3. Problem of the Day
How can you cut the rectangular prism into 8 pieces of equal volume by making only 3 straight cuts?

4. Sunshine State Standards
MA.7.G.2.1 Justify and apply formulas for… volume of…prisms [and] cylinders…
Also MA.7.G.2.2

5. Vocabulary
volume

6. Any three-dimensional figure can be filled completely with congruent cubes and parts of cubes. The volume of a three-dimensional figure is the number of cubes it can hold. Each cube represents a unit of measure called a cubic unit.

7. To find the volume of a rectangular prism, you can count cubes or multiply the lengths of the edges.

9. Additional Example 1A: Using a Formula to Find the Volume of a Prism
Find the volume of the figure.
V = Bh
Use the formula.
The base is a square: B = 4  4 = 16.
V = 16  12
Substitute for B and h.
V = 192
Multiply.
The volume of the prism is 192 ft3.

10. Additional Example 1B: Using a Formula to Find the Volume of a Prism
Find the volume of the figure.
V = Bh
Use the formula.
The base is a triangle: B = 1/2  16  6 = 48.
V = 48  8
Substitute for B and h.
V = 384
Multiply.
The volume of the triangular prism is 384 yd3.

11. Check It Out: Example 1A
Find the volume of each figure to the nearest tenth.
b = 6.3(8) = 50.4
V = Bh = 50.4(6.3) =
≈ ft3.

12. Check It Out: Example 1B
Find the volume of each figure to the nearest tenth.
V = Bh 1 2
B = (13)(10) = 65
V = (65)(50) = 3250
≈ m3.

13. Reading Math
Any unit of measurement with an exponent of 3 is a cubic unit. For example, m3 means “cubic meter” and in3 means “cubic inch.”

14. Finding the volume of a cylinder is similar to finding
the volume of a prism.

15. Additional Example 2: Using a Formula to Find the Volume of a Cylinder
A can of tuna is shaped like a cylinder. Find its volume to the nearest tenth. Use 3.14 for .
V = r2h
Use the formula.
The radius of the cylinder is 5 m, and
the height is 4.2 m
V  3.14 · 52 · 4.2
Substitute for r and h.
V  329.7
Multiply.
The volume is about m3.

16. Find the volume of the cylinder to the nearest tenth. Use 3.14 for .
Check It Out: Example 2
Find the volume of the cylinder to the nearest tenth. Use 3.14 for .
7 ft
3.8 ft
V = r2h  (3.14)(7)2(3.8) 
 ft3.

17. Additional Example 3: Finding The Volume of a Composite Figure
Find the volume of the composite figure to the nearest ft. Use 3.14 for .
Volume of a composite figure
Volume of prism
Volume of triangular prism = + V = Bh + Bh
V  (4)(6)(12) + (½)(4)(6) · (6)‏
V 
V  ft3

18. Check It Out: Example 3A
Assume that the prism from Exercise 1a has been stacked on top of the cylinder from Exercise 2. Find the volume of the composite figure to the nearest tenth. Use 3.14 for .
V  Bh +  r2h  
 ft3

19. volume of the composite figure to the nearest tenth. Use 3.14 for .
Check It Out: Example 3B
The triangular faces of a triangular prism have a height of 5 m and a base of 8 m. The height of the prism is 10 m. The triangular prism is connected to a cylinder. The height of the cylinder is 4 m and the radius is 6 m. Find the
volume of the composite figure to the nearest tenth. Use 3.14 for .
V  Bh +  r2h
B  (8)(5) = 20
 m3 1 2
V  (20)(10) + (3.14)(6)2 (4) 

20. Lesson Quiz for Student Response Systems
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems 20 20

21. Lesson Quiz
1. Find the volume of the prism.
792 cm3
2. A storage tank is shaped like a cylinder. Find its volume to the nearest tenth. Use 3.14 for .
4,069.4 cm3
3. Find the volume of the composite figure.
216 in3

22. Lesson Quiz for Student Response Systems
1. Identify the volume of the prism.
A. 35 cm3
B. 95 cm3
C. 133 cm3
D. 665 cm3 22 22

23. Lesson Quiz for Student Response Systems
2. A piece of wood is shaped like a cylinder. Find its volume to the nearest tenth. Use 3.14 for .
A cm3
B cm3
C. 414 cm3
D. 207 cm3 23 23