Unit 7: Solid Figures
and Measurement
Now’s the time to SHAPE UP!!
March 17, 2011
1) Write your homework in your agenda:
HWP workbook Lesson 10-7 and 10-8
#2, 4, 6 on each page
2) Open your agenda to your behavior
card.
3) Take out your surface area worksheet,
put your name on it and leave it on your
desk.
What am I Learning Today?
Volume
How will I show that I learned it?
Determine the formula for finding the volume
of fundamental solid figures
Compute volume using formulas and
appropriate units of measure
Solve application problems involving volume
Vocabulary
 Volume:
The number of cubic units needed
to fill a given space.
What exactly does this mean?
It takes 10 centimeter cubes to
cover the bottom layer of this
rectangular prism (5cm x 2cm).
It will take 3 layers of 10 cubes
each to fill the prism. It takes
30 cubes or (5cm · 2cm · 3cm).
Volume is expressed in cubic
units, so the volume of the prism
is 5 cm · 2 cm · 3 cm = 30 cm3.
Volume of a Rectangular Prism
h
VV==lBh
xwxh
Volume
Base Area
Base Area
Height
What is the shape of the base here?
What is the formula for its area?
(Remember the “Base Area” formula will be determined by the base shape.)
B=lxw
Replace the “B” with l x w
Volume of a Cylinder
Base Area
Radius
VV==Bh
rh
2
Base Area
Height
Volume
h What is the shape of the base here?
What is the formula for its area?
B = r
Base
Area
2
Radius
Replace the “B”
2
with  (r)
Questions
How do I find the
volume for any
prism or cylinder?
Answers
Use the formula V= Bh, where B is the area of the base,
and h is the height.
V =Bh or l x w x h
2m
What is the formula
for the volume of a
rectangular prism ?
V= Bh or l x w x h
V= 6 x 5 or 3 x 2 x 5
V= 30 m3
5m
3m
What is the
volume of a
cylinder?
V = Bh or TTr2h
2 cm
4 cm
V
V
V
V
=
=
=
=
Bh or TTr2h
3.14 x 22 x 4
3.14 x 4 x 4
3.14 x 16 = 50.24 cm3
Find the volume of the rectangular prism.
16 in.
12 in.
29 in.
V = Bh or V = l x w x h
V = 29
•
V = 348
12
•
•
16
V = 5,568 in3
16
Write the formula.
Substitute the values.
l = 29 w = 12 h = 16
Multiply and label correctly.
Finding the Volume of a Cylinder
Find the volume of a cylinder with height 10 cm
and radius 5cm.
5 cm
V = Bh
B  r
2
B   (5)
2
B  25  cm
10 cm
2
V = Bh
V  25  (10 )
V  250  cm
3
Find which cylinder has the
greater volume.
Cylinder 1:
V = r2h
V  3.14  (1.5)2  12
V  84.78 cm3
Cylinder 2:
V = r2h
V  3.14  32  6
V  169.56 cm3
Cylinder 2 has the greater volume because
169.56 cm3 > 84.78 cm3.
Now Try This!!
Find the volume of each figure.
1) Rectangular prism with length of 20 cm,
width of 15 cm, and height of 12 cm.
V =3,600 cm3
2) Cylinder with radius = 3.2 ft, height = 6 ft
V = 192.92 ft3
March 17, 2011
1) Write your homework in your agenda:
NONE
2) Open your agenda to your behavior
card.
3) Take out your HWP workbook, open to
p. 89 and 90 and leave it on your desk.
Volume of a Pyramid
V = 1/3
x w x h)
V =(l⅓Bh
h
Volume
Base Area
Height
What is the shape of the base here?
What is the formula for its area?
(Remember the “Base Area” formula will be determined by the base shape.)
Base Area
B=lxw
Replace the “B”
with l x w
What do you notice about the relationship between
the volume of a pyramid and a prism?
Volume of a Cone
⅓Bh
VV==1/3(
 r h)
2
Volume
Base Area
h
r
Height
What is the shape of the base here?
What is the formula for its area?
B = r
Base Area
2 Replace the “B”
2
with  (r)
Radius
What do you notice about the relationship between
the volume of a cone and a cylinder?
Questions
What is the formula
for the volume of a
pyramid ?
Answers
V = 1/3 Bh or 1/3 (l x w x h)
3 cm
4 cm
What is the
volume of a
cone?
2 cm
V= 1/3 Bh or 1/3 (l x w x h)
V= 1/3 (8 x 3) or 1/3 (4 x 2 x 3)
V= 1/3 (24)
V = 8 cm3
V = 1/3 Bh or 1/3 (TTr2h)
4 cm
2 cm
V
V
V
V
V
V
=
=
=
=
=
=
1/3 Bh or 1/3 (TTr2h)
1/3 (3.14 x 22 x 4)
1/3 (3.14 x 4 x 4)
1/3 (12.56 x 4)
1/3 (50.24)
16.746 cm3
Find the volume of the pyramid.
V = 1/3 Bh or 1/3 (l x w x h)
V = 1/3 (14
•
V = 1/3 (140
10
•
•
19)
19)
V = 1/3 (2660)
V = 886.67 cm3
Finding the Volume of a Cone
The radius of the base of a cone is 6 m.
Its height is 13 m. Find the volume.
V = ⅓Bh
B  r
2
B   6 
2
B  36  m
2
V = ⅓Bh
V 
1
( 36  )( 13 )
3
V  156  m
3
13 m
6m
Find the volume of the cone.
V = 1/3 Bh or 1/3 (TTr2h)
V  1/3 (3.14  42  16)
V  1/3 (3.14  16  16)
V  1/3 (50.24  16)
V  1/3 (803.84)
V  267.95 cm3
Now Try This!!
Find the volume of each figure.
1) Pyramid with a height of 4 m, a length of 2.5 m
and width of 2 m.
V =6.67 m3
2) Cone with diameter = 4 in, height = 6 in
V = 25.12 in3