Unit 7: Solid Figures and Measurement

1
Unit 7 Solid Figures and Measurement

• Nows the time to SHAPE UP!!

2
Warm-Ups Jim-Bob went to visit Ellie Mae at the
pet store where she worked. Her boss had asked
her to divide 36 goldfish, 42 guppies, and 126
white fish equally into as many aquariums as
possible. What is the greatest number of
aquariums she can fill?
3
Warm-Ups Lovey hears that Jim-Bob is dating Ellie
May. She calls Jim-Bob and wants to get back
together.
4
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
5
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.
6
Volume of a Rectangular Prism
V Bh
h
Volume
Height
Base Area
Base Area
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 l x w
7
Find the volume of the rectangular prism.
16 in.
12 in.
29 in.
V Bh or V l x w x h
Write the formula.
Substitute the values. l 29 w 12 h 16
V 29 12 16
V 348 16
Multiply and label correctly.
V 5,568 in3
8
Practice
Volume of cubes and rectangular prisms
http//www.thatquiz.org/tq-4/?-j20k0-la-n35-p0
Volume and Surface Area mixed
http//www.thatquiz.org/tq-4/?-j24u0-la-n35-p0
9
Questions Answers
Questions Notes
How do I find the volume for any prism or
cylinder?
Use the formula V Bh, where B is the area of the
base, and h is the height.
2 m
V Bh or l x w x h
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
5 m
3 m
What is the volume of a cylinder?
V Bh or TTr2h
2 cm
V Bh or TTr2h V 3.14 x 22 x 4 V 6.28 x 4 x
4 V 25.12 x 4 100.48 cm3
4 cm
10
Volume of a Cylinder
Radius
V Bh
Base Area
Base Area
Height
h
Volume
B ? r2
Base Area
Radius
11
Find the volume of the cylinder to the nearest
cubic unit.
6 ft
5 ft
V Bh or ?r2h
Write the formula.
12
Finding the Volume of a Cylinder

• Find the volume of a cylinder with height 10 cm
  and radius 5cm.

5 cm
V Bh
10 cm
V Bh
13
Find which cylinder has the greater
volume. Cylinder 1
Cylinder 2
14
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.
• 2) Cylinder with radius 3.2 ft, height 6 ft

15
Practice
Volume of Cylinders
http//www.thatquiz.org/tq-4/?-j2800-la-n35-p0
Volume and Surface Area mixed
http//www.thatquiz.org/tq-4/?-j2cu0-la-n35-p0
16
Questions Answers
Questions Notes
V 1/3 Bh or 1/3 (l x w x h)
What is the formula for the volume of a pyramid ?
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
3 cm
4 cm
2 cm
What is the volume of a cone?
V 1/3 Bh or 1/3 (TTr2h)
V 1/3 Bh or 1/3 (TTr2h) V 1/3 (3.14 x 22 x
4) V 1/3 (3.14 x 4 x 4) V 1/3 (12.56 x 4) V
1/3 (50.24) V 16.746 cm3
4 cm
2 cm
17
Volume of a Pyramid
V ?Bh
Base Area
h
Height
Volume
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 l x w
What do you notice about the relationship between

the volume of a pyramid and a prism?
18
Find the volume of the pyramid.
V 1/3 Bh or 1/3 (l x w x h)
V 1/3 (14 10 19)
V 1/3 (140 19)
V 1/3 (2660)
V 886.67 cm3
19
Volume of a Cone
V ?Bh
Height
Volume
Base Area
h
B ? r2
r
Radius
Base Area
What do you notice about the relationship between

the volume of a cone and a cylinder?
20
Find the volume of the cone.
V 1/3 Bh or 1/3 (TTr2h)
21
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 ?Bh
V ?Bh
22
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.
• 2) Cone with diameter 4 in, height 6 in

23
Practice
Volume of Cones
http//www.thatquiz.org/tq-4/?-j3000-la-n35-p0
Volume and Surface Area mixed
http//www.thatquiz.org/tq-4/?-j3cu1-la-n35-p0