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