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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 ft4 ft
3 ft
5 + 4 + 3 = 12 ft
When you measure circumference, you are also
measuring length.
4 cm4 x 3.14 = 12.56cm
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.
3 in
4 in
The area of this rectangle is 12 square inches
3 in
4 in
Now, suppose that we “stacked” another piece of paper on top of this
piece of paper.
3 in
4 in
3 in
4 in
3 in
4 in
3 in
4 in
3 in
4 in
3 in
4 in
Now we have 2 pieces of paper, each with an area of 12. So the
volume is 24.
3 in
4 in
Let’s add another piece of paper to the stack.
3 in
4 in
3 in
4 in
3 in
4 in
3 in
4 in
3 in
4 in
3 in
4 in
Now we have 3 pieces of paper, each with an area of 12. So the
volume is 36.
If we had 100 pieces of paper stacked on top of one another,
what would the volume be?
4 in
3 in
100
4 x 3 x 100 = 1200
4 in
3 in
100
What are the units for volume?
Now that we are working with
all 3 dimensions, the units are cubes.
This is 1 cubic inch.1 x 1 x 1
1 in1 in
1 in
This is 2 cubic inches.2 x 1 x 1
2 in1 in
1 in
This is 4 cubic inches.2 x 1 x 2
2 in
1 in
2 in
2 in
2 in
2 in
8 cubic inches 2 x 2 x 2
Calculate the volume of this prism.
5 cm
8 cm6 cm
The volume is 240 cubic cm.6 x 5 x 8
5 cm
8 cm6 cm
Calculate the volume of this prism.
3 cm
12 cm5 cm
The volume is 180 cubic cm.5 x 3 x 12
3 cm
12 cm5 cm
Calculate the volume of this prism.
4 cm
11 cm7 cm
The volume is 308 cubic cm.7 x 4 x 11
4 cm
11 cm7 cm
Volume can also be described as AREA x Height
Suppose that the area of this rectangle is 12.
4
3
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.
SUMMARYVolume = Length x Width x Height
orVolume = Area of Base x Height
Practice Time!
1) Find the volume of the prism.
3 cm
3 cm
8 cm
The volume is 72 cm3.3 x 8 x 3
3 cm
3 cm
8 cm
2) Find the volume of the prism.
5 in
5 in
12 in
The volume is 300 in3.12 x 5 x 5
5 in
5 in
12 in
3) Find the volume of the prism.
2.5 ft
Area = 20 ft2
base
base
Volume = area x heightVolume = 20 x 2.5 = 50 ft3
2.5 ft
Area = 20 ft2
basebase
4) Find the volume of the prism.
14 m
Area = 12 m2
basebase
Volume = area x heightVolume = 12 x 14 = 168 m3
14 m
Area = 12 m2
base
base
5) Find the volume of the prism.
25 cm
Area = 15 cm2
basebase
Volume = area x heightVolume = 15 x 25 = 375 cm3
25 cm
Area = 15 cm2
basebase
6) Find the volume of the cylinder.
10 in
Area = 78.5 in2
base
base
Volume = area x heightVolume = 78.5 x 10 = 785 in3
10 in
Area = 78.5 in2
base
base
7) Find the volume of shape.
12 m
Area = 36.2 m2
basebase
Volume = area x heightVolume = 36.2 x 12 = 434.4 m3
12 m
Area = 36.2 m2
basebase
8) Find the volume of the triangular prism.
10ft15ft
8ft
Area of base = 8 x 10 ÷ 2 = 40 ft2
40 x 15 = 600 ft3
10ft15ft
8ft
9) Find the volume of the triangular prism.
8m12m
6m
8m12m
6m
Area of base = 6 x 8 ÷ 2 = 24 ft2
24 x 12 = 288 m3
10) Find the volume of the triangular prism.
7 cm11 cm
6cm
7 cm11 cm
6cm
Area of base = 6 x 7 ÷ 2 = 21 ft2
21 x 11 = 231 m3
11) Find the volume of the cylinder.
6 in
3 in
Area of base = 3 x 3 x 3.14 = 28.26 in2
28.26 x 6 = 169.56 in3
6 in
3 in
12) Find the volume of the cylinder.
8 km
5 km
8 km
5 km
Area of base = 5 x 5 x 3.14 = 78.5 km2
78.5 x 8 = 628 km3
13) Find the volume of the cylinder.
11 m
8 m
11 m
8 m
Area of base = 8 x 8 x 3.14 = 200.96 m2
200.96 x 11 = 2210.56 m3
THE END!
