1. Volumes of Prisms & Cylinders

2. Volume Volume – Is the space that a figure occupies.
Measured in cubic units.
cm3, in3, m3, ft3

3. Finding the volume of a Prism
Prism – 2  parallel bases and faces are rectangles. Cross sections are congruent to the bases. What is a Cross section?
V = Bh
Height of Prism
Area of Base or Cross Section
A = lw (Rectangle)
Height (h)
Area of Base (B)

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

6. Discussion: What prism is this. Look at the Cross Section to determine
Discussion: What prism is this? Look at the Cross Section to determine. Why can’t you use l • w • h?
3 in
10in
V = Bh
= ½bh • h
= ½(8in) __ • (10in)
= (12in2) • (10in)
= 120in3
8in
3in

7. Now work on this prism! It’s tricky so be careful.
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
a = 21

8. Volume of a Cylinder Video for help: YouTube
Height of cylinder r
V = Bh h
Volume of right cylinder
Area of base or cross section: (Circle)
A = r2

9. Ex.4: Find the area of the following right cylinder.
Area of a Circle
V = Bh
= r2 • h
= 3.14(8ft)2 • (9ft)
= ft2 • (9ft)
= ft3
16ft
9ft

10. 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

11. 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.