Transcript Document

By Dr. Julia Arnold
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What is volume?
Volume is a way of measuring space. For example, how much space is in
a rectangular room that has floor measurements of 12 ft. by 16 ft. and a
wall or height measurement of 12 ft.
To measure space we use a cube
1 ft. by 1 ft. by 1 ft. or
1 cubic foot.
So, how many of these cubes will
it take to fill the above room?
1 ft
1 ft
1 ft.
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sound
Click here for floor plan
12
12
16
We can stack 16 times 12 cubes on the floor or 192 cubes and then
we can stack these 192 cubes 12 layers high for a total of 2304 cubes
measured in feet, so we call it cubic feet.
The volume of our room is 12 * 12* 16= 2304 cubic feet
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sound
A rectangular solid is what you might think of as a box shape. All the sides are
perpendicular to each other and the three dimensions that it has (length, width, and
height) may be different measurements. Formula for volume is V = lwh
h
w
l
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A cube is a rectangular solid in which all of the sides are equal in length. Formula for
volume is V = e3 where e is the measure of a side.
e
e
e
e
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A sphere is what you would think of as a ball, no sharp edges, round all over. Formula
for the volume of a sphere is
where r is the radius of the sphere.
4 3
V  r
3
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sound
A cylinder is what we might think of as a can. While we may have in mathematics
slanted cans, the ones in the store are what we call a right circular cylinder in that the
sides are perpendicular to the horizontal. The base and top of the can is a circle and
thus has a radius r, the distance between the top and bottom is called the height of
the can or h. If cut and straightened out this shape would be a rectangle.
Area of top is  r
2
V  r h
2
h
r
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sound
A right circular cone is similar to an ice cream cone.
In mathematics there are slanted cones, but for our purposes we will be looking at
the right circular cone,
whose base (which is a circle) is perpendicular to the
horizontal.
R is the radius at
the base of the
cone.
H is the height of
the cone.
r
The formula for
the volume is
h
1 2
V  r h
3
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for
sound
Use the formulas to compute the volume of the objects in the following problems.
When necessary round your answers to the nearest hundredth. When writing your
final answer, use the appropriate units, i.e. cu ft. A new convention for writing
cubic units or square units is to use an exponent on the type of unit, for example;
cubic feet would be written ft3.
When finished check your answers on the last page.
1. Rectangular solid: L = 73mm, W = 17.2 mm, H = 16 mm
(mm is millimeters)
2. Cube: e = 17.3 in (inches)
In = inches, cm = centimeters, m = meters
d= diameter of circle = 2 r or 2 radii
3. Sphere: r = 8.2 in
4. Sphere: diameter= 76.4 cm
5. Cylinder: r = 13.5 in, h = 8.2 in
6. Cylinder: d = 16.2 m, h = 7.5 m
7. Cone: r = 1.4 cm, h = 5 cm
8. Cone: d = 9.5 in, h = 7 in
Work out these problems before going to the next slide.
1. Rectangular solid: L = 73mm, W = 17.2 mm, H = 16 mm
(mm is millimeters)
20,089.6 mm3
5177.72 in3
2. Cube: e = 17.3 in (inches)
3. Sphere: r = 8.2 in
4. Sphere: diameter= 76.4 cm
5. Cylinder: r = 13.5 in, h = 8.2 in
6. Cylinder: d = 16.2 m, h = 7.5 m
7. Cone: r = 1.4 cm, h = 5 cm
8. Cone: d = 9.5 in, h = 7 in
2309.56 in3
233,495.60 cm3
4694.95 in3
1545.90 m3
10.26 cm3
165.39 in3
Congratulations! You have just completed
the geometry unit.