1. Lesson 11.3
Cylinders pp

2. Objectives: 1. To derive the formula for the volume of a cylinder.
2. To apply the formula to specific cylinders.

5. Theorem 11.4
The volume of a cylinder is the product of the area of a base and the height: V = BH. In particular, for a circular cylinder V = r2H.

6. EXAMPLE Find the volume.12 5
V = r2H
V = (5)2(12)
V = 300
V ≈ in3

7. Practice: Find the volume. Assume the base is circular.
C = 24 in
16 in
C = 2r
24 = 2r
r = 12

8. Practice: Find the volume. Assume the base is circular.
C = 24 in
16 in
V = r2H
V = (12)2(16)
V = 2304
V  in3

9. Practice: Find the volume. Assume the base is circular.
2 mm
4 cm
d = 4 cm
r = 2 cm
r = 20 mm
V = r2H
V = (20)2(2)
V = 800
V ≈ mm3

10. Homework pp

11. Find the volume of each cylinder. 1.
►A. Exercises
Find the volume of each cylinder. 1. 7 9

12. Find the volume of each cylinder. 5.
►A. Exercises
Find the volume of each cylinder. 5. 11 19

13. ►A. Exercises
9. A cylinder is lodged inside a
square prism similar to the figure
shown. How many inches are
within the prism but outside the
cylinder?

14. ►A. Exercises 9. Vprism = BH = 182(26) = 8424 Vcylinder = BH
= 182(26)
= 8424
Vcylinder = BH
= (92)(26)
= 2106
V = Vp – Vc
= 
≈ un3 9 26

15. ►B. Exercises
11. The circumference of a cylinder is
86 meters, and the height is 63
meters. Find the surface area and
volume of the cylinder.
C = 2r
86 = 2r
43 = r

16. ►B. Exercises
11. The circumference of a cylinder is
86 meters, and the height is 63
meters. Find the surface area and
volume of the cylinder.
V = BH
B = r2 = 432 = 1849
V = 1849(63) = 116,487 m3

17. ►B. Exercises
11. The circumference of a cylinder is
86 meters, and the height is 63
meters. Find the surface area and
volume of the cylinder.
S = L + 2B
L = cH = 86(63) = 5418
S = 5418 + 2(1849)
= 9116 m2

18. ►B. Exercises
13. A cylindrical piece of iron has a diameter of 2 inches and a length of 16 inches. If it is melted down and poured into a rectangular mold that has a 1-by-3 base, what will be the length of the rectangular piece of iron?

19. ►B. Exercises
15. How many cubic yards of concrete
are needed to pour the patio and
sidewalk if the thickness is to be
four inches?

20. Patio 6’
10’ 8’ 3’
24’
►B. Exercises
15.

21. ■ Cumulative Review 25. circular cylinder
Identify the horizontal cross section for each of the following figures.
25. circular cylinder

22. ■ Cumulative Review 26. parallelepiped
Identify the horizontal cross section for each of the following figures.
26. parallelepiped

23. ■ Cumulative Review 27. tetrahedron
Identify the horizontal cross section for each of the following figures.
27. tetrahedron

24. ■ Cumulative Review 28. circular cone
Identify the horizontal cross section for each of the following figures.
28. circular cone

25. ■ Cumulative Review 29. sphere
Identify the horizontal cross section for each of the following figures.
29. sphere