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

2. Warm Up Find the volume of each figure described.
1. rectangular prism with length 12 cm, width 11 cm, and height 10 cm
1,320 cm3
2. triangular prism with height 11 cm and triangular base with base length 10.2 cm and height 6.4 cm
cm3

3. Problem of the Day
The height of a box is half its width. The length is 12 in. longer than its width. If the volume of the box is 28 in3, what are the dimensions of the box?
1 in.  2 in.  14 in.

4. Learn to find volumes of cylinders.

5. To find the volume of a cylinder, you can use the same method as you did for prisms: Multiply the area of the base by the height.
volume of a cylinder = area of base  height
The area of the circular base is r2, so the formula is V = Bh = r2h.

6. Additional Example 1A: Finding the Volume of a Cylinder
Find the volume V of the cylinder to the nearest cubic unit.
V = r2h
Write the formula.
V  3.14  42  7
Replace  with 3.14, r with 4, and h with 7.
V 
Multiply.
The volume is about 352 ft3.

7. Additional Example 1B: Finding the Volume of a Cylinder
10 cm ÷ 2 = 5 cm
Find the radius.
V = r2h
Write the formula.
V  3.14  52  11
Replace  with 3.14, r with 5, and h with 11.
V  863.5
Multiply.
The volume is about 864 cm3.

8. Additional Example 1C: Finding the Volume of a Cylinder3 __
Find the radius.
r = = 7 9 3 __
Substitute 9 for h.
V = r2h
Write the formula.
V  3.14  72  9
Replace  with 3.14, r with 7, and h with 9.
V  1,384.74
Multiply.
The volume is about 1,385 in3.

9. Check It Out: Example 1A
Find the volume V of each cylinder to the nearest cubic unit.
6 ft
5 ft
V = r2h
Write the formula.
V  3.14  62  5
Replace  with 3.14, r with 6, and h with 5.
V  565.2
Multiply.
The volume is about 565 ft3.

10. Check It Out: Example 1B
8 cm
6 cm
8 cm ÷ 2 = 4 cm
Find the radius.
V = r2h
Write the formula.
V  3.14  42  6
Replace  with 3.14, r with 4, and h with 6.
V 
Multiply.
The volume is about 301 cm3.

11. Check It Out: Example 1C h
r = 4
h = 8 in
r = h 4 __
Find the radius.
r = = 7 8 4 __
Substitute 8 for h.
V = r2h
Write the formula.
V  3.14  72  8
Replace  with 3.14, r with 7, and h with 8.
V  1,230.88
Multiply.
The volume is about 1,231 in3.

12. Additional Example 2A: Application Ali has a cylinder-shaped pencil holder with a 3 in. diameter and a height of 5 in. Scott has a cylinder- shaped pencil holder with a 4 in. diameter and a height of 6 in. Estimate the volume of each cylinder to the nearest cubic inch.
Ali’s pencil holder
3 in. ÷ 2 = 1.5 in.
Find the radius.
V = r2h
Write the formula.
Replace  with 3.14, r with 1.5, and h with 5.
V  3.14  1.52  5
V 
Multiply.
The volume of Ali’s pencil holder is about 35 in3.

13. Additional Example 2B: Application
Scott’s pencil holder
4 in. ÷ 2 = 2 in.
Find the radius.
V = r2h
Write the formula.
Replace  with , r with
2, and h with 6. 22 7 __ 22 7 __
V   22  6
V  = 75
528 7
___ 3 __
Multiply.
The volume of Scott’s pencil holder is about 75 in3.

14. Replace  with 3.14, r with 1.5, and h with 6. V  3.14  1.52  6
Check It Out: Example 2A
Sara has a cylinder-shaped sunglasses case with a 3 in. diameter and a height of 6 in. Ulysses has a cylinder-shaped pencil holder with a 4 in. diameter and a height of 7 in. Estimate the volume of each cylinder to the nearest cubic inch.
Sara’s sunglasses case
3 in. ÷ 2 = 1.5 in.
Find the radius.
V = r2h
Write the formula.
Replace  with 3.14, r with 1.5, and h with 6.
V  3.14  1.52  6
V  42.39
Multiply.
The volume of Sara’s sunglasses case is about 42 in3.

15. Check It Out: Example 2B
Ulysses’ pencil holder
4 in. ÷ 2 = 2 in.
Find the radius.
V = r2h
Write the formula.
Replace  with , r with
2, and h with 7. 22 7 __
V   22  7 22 7 __
V  88
Multiply.
The volume of Ulysses’ pencil holder is about 88 in3.

16. Additional Example 3: Comparing Volumes of Cylinders Find which cylinder has the greater volume.
V = r2h
V  3.14  1.52  12
V  cm3
Cylinder 2:
V = r2h
V  3.14  32  6
V  cm3
Cylinder 2 has the greater volume because
cm3 > cm3.

17. Find which cylinder has the greater volume.
Check It Out: Example 3
Find which cylinder has the greater volume.
Cylinder 1:
V = r2h
10 cm
2.5 cm
4 cm
V  3.14  2.52  10
V  cm3
Cylinder 2:
V = r2h
V  3.14  22  4
V  cm3
Cylinder 1 has the greater volume because
cm3 > cm3.

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

19. Lesson Quiz: Part I
Find the volume of each cylinder to the nearest cubic unit. Use 3.14 for .
1. radius = 9 ft, height = 4 ft
1,017 ft3
2. radius = 3.2 ft, height = 6 ft
193 ft3
3. Which cylinder has a greater volume?
a. radius 5.6 ft and height 12 ft
b. radius 9.1 ft and height 6 ft
cylinder b
1, ft3
1, ft3

20. Lesson Quiz: Part II
4. Jeff’s drum kit has two small drums. The first drum has a radius of 3 in. and a height of 14 in. The other drum has a radius of 4 in. and a height of 12 in. Estimate the volume of each cylinder to the nearest cubic inch.
a. First drum
b. Second drum
about 396 in2
about 603 in2

21. Lesson Quiz for Student Response Systems
1. Identify the volume of a cylinder with a radius of 11 ft and a height of 5 ft to the nearest cubic unit. Use 3.14 for .
A. 1,900 ft3
B. 1,890 ft3
C. 1,706 ft3
D. 690 ft3

22. Lesson Quiz for Student Response Systems
2. Identify the volume of a cylinder with a radius of 4.3 ft and a height of 5 ft to the nearest cubic unit. Use 3.14 for .
A. 338 ft3
B. 305 ft3
C. 297 ft3
D. 290 ft3

23. Lesson Quiz for Student Response Systems
3. A mechanic uses two small iron tubes. The first tube has a radius of 4 in. and a height of 12 in. The other tube has radius of 5 in. and a height of 10 in. Estimate the volume of each tube to the nearest cubic inch.
A. first tube: about 942 in3; second tube: about 502 in3 B. first tube: about 603 in3; second tube: about 502 in3
C. first tube: about 942 in3; second tube: about 785 in3
D. first tube: about 603 in3; second tube: about 785 in3