1. 7.5 Volume of Prisms and Cylinders
MA 08Geometry
7.5 Volume of Prisms and Cylinders

2. Geometry 12.4 Volume of Prisms and Cylinders
Goals
Find the volume of prisms.
Find the volume of cylinders.
Solve problems using volume.
Monday, May 5, 2:51
Geometry 12.4 Volume of Prisms and Cylinders

3. Geometry 12.4 Volume of Prisms and Cylinders
The number of cubic units contained in a solid.
Measured in cubic units.
Basic Formula:
V = Bh
B = area of the base, h = height
Monday, May 5, 2:51
Geometry 12.4 Volume of Prisms and Cylinders

4. Geometry 12.4 Volume of Prisms and Cylinders
Cubic Unit
V = s3
V = 1 cu. unit s 1 1 s 1 s
Monday, May 5, 2:51
Geometry 12.4 Volume of Prisms and Cylinders

5. Geometry 12.4 Volume of Prisms and Cylinders
Prism: V = Bh B B h h h B
Monday, May 5, 2:51
Geometry 12.4 Volume of Prisms and Cylinders

6. Geometry 12.4 Volume of Prisms and Cylinders
Cylinder: V = r2h r B h h
V = Bh
Monday, May 5, 2:51
Geometry 12.4 Volume of Prisms and Cylinders

7. Example 1 Find the volume.
Triangular Prism
V = Bh
Base = 40
V = 40(3) = 120 10 8 3
Abase = ½ (10)(8) = 40
Monday, May 5, 2:51
Geometry 12.4 Volume of Prisms and Cylinders

8. Geometry 12.4 Volume of Prisms and Cylinders
Example 3
A soda can measures 4.5 inches high and the diameter is 2.5 inches. Find the approximate volume.
V = r2h
V = (1.252)(4.5)
V  22 in3
(The diameter is 2.5 in. The radius is 2.5 ÷ 2 inches.)
Monday, May 5, 2:51
Geometry 12.4 Volume of Prisms and Cylinders

9. Geometry 12.4 Volume of Prisms and Cylinders
Example 4
A wedding cake has three layers.
The top cake has a diameter of 8 inches, and is 3 inches deep.
The middle cake is 12 inches in diameter, and is 4 inches deep.
The bottom cake is 14 inches in diameter and is 6 inches deep.
Find the volume of the entire cake, ignoring the icing.
Monday, May 5, 2:51
Geometry 12.4 Volume of Prisms and Cylinders

10. Geometry 12.4 Volume of Prisms and Cylinders
Example 4 Solution
VTop = (42)(3) = 48  in3
VMid = (62)(4) = 144  in3
VBot = (72)(6) = 294  in3
r = 4 8 3
r = 6 12 4
486  in3 14 6
r = 7
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Geometry 12.4 Volume of Prisms and Cylinders

11. Geometry 12.4 Volume of Prisms and Cylinders
Concrete Pipe
Monday, May 5, 2:51
Geometry 12.4 Volume of Prisms and Cylinders

12. Geometry 12.4 Volume of Prisms and Cylinders
Example 5
A manufacturer of concrete sewer pipe makes a pipe segment that has an outside diameter (o.d.) of 48 inches, an inside diameter (i.d.) of 44 inches, and a length of 52 inches. Determine the volume of concrete needed to make one pipe segment. 48 44 52
Monday, May 5, 2:51
Geometry 12.4 Volume of Prisms and Cylinders

13. Geometry 12.4 Volume of Prisms and Cylinders
Example 5 Solution
Strategy:
Find the area of the ring at the top, which is the area of the base, B, and multiply by the height.
View of the Base
Monday, May 5, 2:51
Geometry 12.4 Volume of Prisms and Cylinders

14. Geometry 12.4 Volume of Prisms and Cylinders
Example 5 Solution
Strategy:
Find the area of the ring at the top, which is the area of the base, B, and multiply by the height.
Area of Outer Circle:
Aout = (242) = 576
Area of Inner Circle:
Ain = (222) = 484
Area of Base (Ring):
ABase = 576 - 484 = 92 48 44 52
Monday, May 5, 2:51
Geometry 12.4 Volume of Prisms and Cylinders

15. Geometry 12.4 Volume of Prisms and Cylinders
Example 5 Solution
V = Bh
ABase = B = 92
V = (92)(52)
V = 4784
V  15,021.8 in3 48 44 52
Monday, May 5, 2:51
Geometry 12.4 Volume of Prisms and Cylinders

16. Geometry 12.4 Volume of Prisms and Cylinders
Example 6 4 5 L
A metal bar has a volume of 2400 cm3. The sides of the base measure 4 cm by 5 cm. Determine the length of the bar.
Monday, May 5, 2:51
Geometry 12.4 Volume of Prisms and Cylinders

17. Geometry 12.4 Volume of Prisms and Cylinders
Example 6 Solution 4 5 L
V = L  W  H
2400 = L  4  5
2400 = 20L
L = 120 cm
Monday, May 5, 2:51
Geometry 12.4 Volume of Prisms and Cylinders

18. Geometry 12.4 Volume of Prisms and Cylinders
Summary
The volumes of prisms and cylinders are essentially the same:
V = Bh & V = r2h
where B is the area of the base, h is the height of the prism or cylinder.
Use what you already know about area of polygons and circles for B.
Monday, May 5, 2:51
Geometry 12.4 Volume of Prisms and Cylinders

19. Geometry 12.4 Volume of Prisms and CylindersB h h
V = r2h
V = Bh
These are on your reference sheet.
Monday, May 5, 2:51
Geometry 12.4 Volume of Prisms and Cylinders

20. Geometry 12.4 Volume of Prisms and Cylinders
Which Holds More?
This one!
3.2 in
1.6 in
4 in
4.5 in
2.3 in
Monday, May 5, 2:51
Geometry 12.4 Volume of Prisms and Cylinders

21. Geometry 12.4 Volume of Prisms and Cylinders
What would the height of cylinder 2 have to be to have the same volume as cylinder 1?
r = 3
r = 4 #2 #1 8 h
Monday, May 5, 2:51
Geometry 12.4 Volume of Prisms and Cylinders

22. Geometry 12.4 Volume of Prisms and Cylinders
Solution
r = 4 #1 8
Monday, May 5, 2:51
Geometry 12.4 Volume of Prisms and Cylinders

23. Geometry 12.4 Volume of Prisms and Cylinders
Solution
r = 3 #2 h
Monday, May 5, 2:51
Geometry 12.4 Volume of Prisms and Cylinders