1. Volumes of Prisms & Cylinders
Objectives:
1) To find the volume of a prism.
2) To find the volume of a cylinder.

2. Volume Volume – Is the space that a figure occupies.
Measured in cubic units.
cm3, in3, m3, ft3
Th(10-5) Cavalieri’s Principle
If 2 space figures have the same height & the same cross-sectional every level, then they have the same volume.

3. V = Bh I. Finding the volume of a Prism
Prism – 2  parallel bases, sides (Lats) are rectangles.
V = Bh
Height of Prism
Area of Base
A = bh (Rectangle)
A = ½bh (Triangle)
A = ½ap (Polygon)
Height (h)
Area of Base (B)

4. Ex. 1: Finding the Volume of a rectangular prism
The box shown is 5 units long, 3 units wide, and 4 units high. How many unit cubes will fit in the box? What is the volume of the box?

5. Ex.1: Find the Volume of the Prism
Area of Base
B = l•w
V = Bh
= (3in • 5in)(10in)
= (15in2)(10in)
= 150in3
10in
3in
5in

6. Ex.2: Find the volume of the following
Triangle
29m
V = Bh
= ½bh • h
= ½(20m)__ • (40m)
= 210m2 • 40m
= 8400m3 a
40m 21
20m
Height of the base:
a2 + b2 = c2
a = 292
b = 21

7. Ex.3: Yet another prism! Find the volume.8 h
60° 4
10in
Sin 60 = h/8
.866 = h/8
6.9 = h
V = Bh
= ½bh • h
= ½(8in) __ • (10in)
= (27.7in2) • (10in)
= 277in3
8in
6.9

8. Finding Volumes of prisms and cylinders.
Bonaventura Cavalieri ( ). To see how it can be applied, consider the solids on the next slide. All three have cross sections with equal areas, B, and all three have equal heights, h. By Cavalieri’s Principle, it follows that each solid has the same volume.

9. Cavalieri’s Principle
If two solids have the same height and the same cross-sectional area at every level, then they have the same volume.

10. V = Bh II. Volume of a Cylinder Height of cylinder r h
Volume of right cylinder
Area of base: (Circle)
A = r2

11. V = Bh = r2 • h = (8ft)2 • (9ft) = 64ft2 • (9ft) = 576ft3
Ex.4: Find the area of the following right cylinder.
Area of a Circle
V = Bh
= r2 • h
= (8ft)2 • (9ft)
= 64ft2 • (9ft)
= 576ft3
= ft3
16ft
9ft

12. Ex.5: Find the volume of the following composite figure.
Half of a cylinder:
Vc = Bh
= r2•h
= (6in)2 • (4in)
= 452in3
= 452/2 = 226in3
11in
4in
Volume of Prism:
Vp = Bh
= (11)(12)(4)
= 528in3
12in
VT = Vc + Vp
= 226in in3
= 754in3

13. What have we learned?? Volume of a prism or a cylinder: V = Bh
Capitol “B” stands for area of the base.
Composite Figures: Made up of two separate solids.