VOLUME
So far, we have learned
about length. This is a
measure of 1 dimension.
Measuring length can be as
simple as measuring a straight
line segment.
5 inches
When you measure perimeter,
you are also measuring length.
5 ft 5 + 4 + 3 = 12 ft
4 ft
3 ft
When you measure
circumference, you are also
measuring length.
4 x 3.14 = 12.56cm
4 cm
Area is a measure of 2
dimensions:
Length & Width
You can find the area of any
FLAT shape.
5 cm
11 cm
5 x 11 = 55 square cm
You can even find the area of
a circle.
5 cm 5 x 5 x 3.14 =
78.5 sq. cm
Volume is a measure of 3
dimensions:
LENGTH, WIDTH, &
HEIGHT
Imagine starting with a piece
of rectangular paper.
4 in
3 in
The area of this rectangle is
12 square inches
4 in
3 in
Now, suppose that we “stacked”
another piece of paper on top of this
piece of paper.
4 in
3 in
4 in
3 in
4 in
3 in
4 in
3 in
4 in
3 in
Now we have 2 pieces of paper,
each with an area of 12. So the
volume is 24.
4 in
3 in
Let’s add another piece of paper to
the stack.
4 in
3 in
4 in
3 in
4 in
3 in
4 in
3 in
4 in
3 in
4 in
3 in
Now we have 3 pieces of paper,
each with an area of 12. So the
volume is 36.
4 in
3 in
If we had 100 pieces of paper
stacked on top of one another,
what would the volume be?
100
4 in
3 in
4 x 3 x 100 = 1200
100
4 in
3 in
What are the units for volume?
Now that we are working with
all 3 dimensions, the units are cubes.
This is 1 cubic inch.
1x1x1
1 in
1 in
1 in
This is 2 cubic inches.
2x1x1
1 in
1 in
2 in
This is 4 cubic inches.
2x1x2
2 in
1 in
2 in
8 cubic inches 2 x 2 x 2
2 in
2 in
2 in
Calculate the volume of this
prism.
6 cm
8 cm
5 cm
The volume is 240 cubic cm.
6x5x8
6 cm
8 cm
5 cm
Calculate the volume of this
prism.
5 cm
12 cm
3 cm
The volume is 180 cubic cm.
5 x 3 x 12
5 cm
12 cm
3 cm
Calculate the volume of this
prism.
7 cm
11 cm
4 cm
The volume is 308 cubic cm.
7 x 4 x 11
7 cm
11 cm
4 cm
Volume can also be described as
AREA x Height
Suppose that the area of this
rectangle is 12.
3
4
Suppose that this rectangle
served as the base of a
rectangular prism.
Suppose that the prism has a
height of 2.
2
2
2
If the area (length x width) of the
base is 12, and the height is 2…
2
then the volume should be 24
cubic units.
2
Therefore, if you know the area
of the base and the height of the
prism, then you can calculate the
volume.
SUMMARY
Volume = Length x Width x Height
or
Volume = Area of Base x Height
Practice Time!
1) Find the volume of the prism.
3 cm 8 cm
3 cm
The volume is 72 cm3.
3x8x3
3 cm 8 cm
3 cm
2) Find the volume of the prism.
5 in 12 in
5 in
The volume is 300 in3.
12 x 5 x 5
5 in 12 in
5 in
3) Find the volume of the prism.
2.5 ft
base
Area = 20 ft2
Volume = area x height
Volume = 20 x 2.5 = 50 ft3
2.5 ft
base
Area = 20 ft2
4) Find the volume of the prism.
14 m
base
Area = 12 m2
Volume = area x height
Volume = 12 x 14 = 168 m3
14 m
base
Area = 12 m2
5) Find the volume of the prism.
25 cm
base
base
Area = 15 cm2
Volume = area x height
Volume = 15 x 25 = 375 cm3
25 cm
base
base
Area = 15 cm2
6) Find the volume of the
cylinder.
base
base 10 in
Area = 78.5 in2
Volume = area x height
Volume = 78.5 x 10 = 785 in3
base
base 10 in
Area = 78.5 in2
7) Find the volume of shape.
12 m
base
base
Area = 36.2 m2
Volume = area x height
Volume = 36.2 x 12 = 434.4 m3
12 m
base
base
Area = 36.2 m2
8) Find the volume of the triangular
prism.
8ft
15ft
10ft
Area of base = 8 x 10 ÷ 2 = 40 ft2
40 x 15 = 600 ft3
8ft
15ft
10ft
9) Find the volume of the triangular
prism.
6m
12m
8m
Area of base = 6 x 8 ÷ 2 = 24 ft2
24 x 12 = 288 m3
6m
12m
8m
10) Find the volume of the triangular
prism.
6cm
11 cm
7 cm
Area of base = 6 x 7 ÷ 2 = 21 ft2
21 x 11 = 231 m3
6cm
11 cm
7 cm
11) Find the volume of the cylinder.
3 in
6 in
Area of base = 3 x 3 x 3.14 = 28.26 in2
28.26 x 6 = 169.56 in3
3 in
6 in
12) Find the volume of the cylinder.
5 km
8 km
Area of base = 5 x 5 x 3.14 = 78.5 km2
78.5 x 8 = 628 km3
5 km
8 km
13) Find the volume of the cylinder.
8m
11 m
Area of base = 8 x 8 x 3.14 = 200.96 m2
200.96 x 11 = 2210.56 m3
8m
11 m
THE END!