VOLUME

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VOLUME
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So far, we have learned about length. This is a
measure of 1 dimension.
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Measuring length can be as simple as measuring a
straight line segment.
5 inches
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When you measure perimeter, you are also
measuring length.
5 ft
5 4 3 12 ft
4 ft
3 ft
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When you measure circumference, you are also
measuring length.
4 x 3.14 12.56cm
4 cm
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Area is a measure of 2 dimensions Length Width
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You can find the area of any FLAT shape.
5 cm
11 cm
5 x 11 55 square cm
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You can even find the area of a circle.
5 x 5 x 3.14 78.5 sq. cm
5 cm
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Volume is a measure of 3 dimensions LENGTH,
WIDTH, HEIGHT
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Imagine starting with a piece of rectangular
paper.
4 in
3 in
11
The area of this rectangle is 12 square inches
4 in
3 in
12
Now, suppose that we stacked another piece of
paper on top of this piece of paper.
4 in
3 in
13
4 in
3 in
14
4 in
3 in
15
4 in
3 in
16
4 in
3 in
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Now we have 2 pieces of paper, each with an area
of 12. So the volume is 24.
4 in
3 in
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Lets add another piece of paper to the stack.
4 in
3 in
19
4 in
3 in
20
4 in
3 in
21
4 in
3 in
22
4 in
3 in
23
4 in
3 in
24
Now we have 3 pieces of paper, each with an area
of 12. So the volume is 36.
4 in
3 in
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If we had 100 pieces of paper stacked on top of
one another, what would the volume be?
100
4 in
3 in
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4 x 3 x 100 1200
100
4 in
3 in
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What are the units for volume?
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Now that we are working with all 3 dimensions,
the units are cubes.
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This is 1 cubic inch.1 x 1 x 1
1 in
1 in
1 in
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This is 2 cubic inches.2 x 1 x 1
1 in
1 in
2 in
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This is 4 cubic inches.2 x 1 x 2
2 in
1 in
2 in
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8 cubic inches 2 x 2 x 2
2 in
2 in
2 in
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Calculate the volume of this prism.
6 cm
8 cm
5 cm
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The volume is 240 cubic cm.6 x 5 x 8
6 cm
8 cm
5 cm
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Calculate the volume of this prism.
5 cm
12 cm
3 cm
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The volume is 180 cubic cm.5 x 3 x 12
5 cm
12 cm
3 cm
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Calculate the volume of this prism.
7 cm
11 cm
4 cm
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The volume is 308 cubic cm.7 x 4 x 11
7 cm
11 cm
4 cm
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Volume can also be described as AREA x Height
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Suppose that the area of this rectangle is 12.
3
4
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Suppose that this rectangle served as the base of
a rectangular prism.
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Suppose that the prism has a height of 2.
2
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2
44
2
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If the area (length x width) of the base is 12,
and the height is 2
2
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then the volume should be 24 cubic units.
2
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Therefore, if you know the area of the base and
the height of the prism, then you can calculate
the volume.
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SUMMARYVolume Length x Width x
HeightorVolume Area of Base x Height
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Practice Time!
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1) Find the volume of the prism.
3 cm
8 cm
3 cm
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The volume is 72 cm3.3 x 8 x 3
3 cm
8 cm
3 cm
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2) Find the volume of the prism.
5 in
12 in
5 in
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The volume is 300 in3.12 x 5 x 5
5 in
12 in
5 in
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3) Find the volume of the prism.
2.5 ft
base
base
Area 20 ft2
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Volume area x heightVolume 20 x 2.5 50 ft3
2.5 ft
base
base
Area 20 ft2
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4) Find the volume of the prism.
14 m
base
base
Area 12 m2
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Volume area x heightVolume 12 x 14 168 m3
14 m
base
base
Area 12 m2
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5) Find the volume of the prism.
25 cm
base
base
Area 15 cm2
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Volume area x heightVolume 15 x 25 375 cm3
25 cm
base
base
Area 15 cm2
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6) Find the volume of the cylinder.
base
10 in
base
Area 78.5 in2
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Volume area x heightVolume 78.5 x 10 785
in3
base
10 in
base
Area 78.5 in2
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7) Find the volume of shape.
12 m
base
base
Area 36.2 m2
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Volume area x heightVolume 36.2 x 12 434.4
m3
12 m
base
base
Area 36.2 m2
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8) Find the volume of the triangular prism.
8ft
15ft
10ft
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Area of base 8 x 10 2 40 ft240 x 15 600
ft3
8ft
15ft
10ft
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9) Find the volume of the triangular prism.
6m
12m
8m
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Area of base 6 x 8 2 24 ft224 x 12 288 m3
6m
12m
8m
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10) Find the volume of the triangular prism.
6cm
11 cm
7 cm
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Area of base 6 x 7 2 21 ft221 x 11 231 m3
6cm
11 cm
7 cm
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11) Find the volume of the cylinder.
3 in
6 in
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Area of base 3 x 3 x 3.14 28.26 in228.26 x 6
169.56 in3
3 in
6 in
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12) Find the volume of the cylinder.
5 km
8 km
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Area of base 5 x 5 x 3.14 78.5 km278.5 x 8
628 km3
5 km
8 km
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13) Find the volume of the cylinder.
8 m
11 m
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Area of base 8 x 8 x 3.14 200.96 m2200.96 x
11 2210.56 m3
8 m
11 m
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THE END!