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Definition of Volume
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Skills Application: Definition of Volume
Step-by-Step: Definition of Volume
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## Tagged in

The word volume in math refers to the amount of space inside any kind of shape.

Did you know that the price tag of a vehicle is based on this volume concept? Consumers actually pay for the volume of the combustion chamber inside the engine; the more volume an engine has the more expensive the vehicle is.

## Running with Pi

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3. Our Training Worksheets

Trades workers encounter solid or three-dimensional figures in the form of tanks, pipes, ducts, boxes, birthday cakes, and buildings. They must be able to identify these geometric solids and their component parts and compute their volume.

Have you ever had the experience of measuring the amount of space in a tank, a refrigerator or other three-dimensional figures? Volume is the term for measures of the size of three-dimensional figures. It is the amount of space inside an object or the amount of space an object occupies.

A cube is convenient to use as a unit to measure an object’s volume. The number of units needed to fill a figure is its volume.

EXAMPLE

If 1 cubic unit represents 1cm3, what is the volume of the following figure?

SOLUTION

By counting the units, we can figure out the volume of an object. The volume of the figure is 12 cm3 because there are 12 cubic units in it.

Volume is related to length, so units of measure for volume are also related to units of measure for length. Volume like length can be measured in both metric units and inch-based units. Check out the table here to see both systems side by side, symbols, under what other names volume might show up in trades tasks and how volume is different from capacity: See more on capacity vs volume in  Episode 26 ADVANCED.

### A Short Review

Volume or space relates to the size of a 3-D object. Only objects have volume or take up space. Solid objects have one volume, hollow objects have two: a bigger outside and a smaller inside Volume/space, depending on wall thickness of the object. In everyday context the idea of volume or space might be expressed using different words, such as box size, tank size, capacity, trunk size, garment size, serving size, engine size.

Volume or space is usually measured in cube units such as cubic feet, cubic meters, cubic inches.

A cubic foot is a cube with a length of 1 foot, a width of 1 foot and a height of 1 foot.  A cubic cm is a cube with a length of 1 cm, a width of 1 cm and a height of 1 cm.

Some other units of measure don`t seem related to volume first, but they are: bushel, gallon, teaspoon, board foot are all units of volume.

### Worksheet: Level 1

The operations used are clearly specified. Only one type of mathematical operation is used in a task.

### Worksheet: Level 1 Sample Questions

Question:

Which of the following 4 units of measure are used when measuring Volume?

a) m     b) ft³    c) in     d) gallon     e) m²     f) m³     g) ft²     j) cord      k) mi²

Further Examples:

Which of the following things have volume?
1. a table
2. friendship
3. you
4. a credit card
5. π
6. a triangle

Does the volume of the food change from when it is in a messy pile compared to when it is stacked neatly to fit the fridge? Why or why not?

### Worksheet: Level 1 Answer Key

Which of the following 4 units of measure are used when measuring Volume?
a) m     b) ft³    c) in     d) gallon     e) m²     f)      g) ft²     j) cord      k) mi²

### Worksheet: Level 2

Tasks involve one or two types of mathematical operation. Few steps of calculation are required.

### Worksheet: Level 2 Sample Questions

Question:

Understanding concepts of terminology

True or False?

1.  Objects with 6 surfaces have exactly 6 volumes, one for each side.

Further examples:

Which math concept is expressed in the following examples:

Area? Volume? Length?

1. barrel size
2. plate size
3. measuring cup sizes
4. a spill the size of the Grand Canyon
5. sleeve size
6. living room size
7. a box the size of a mouse
8. Celsius degrees
9. cement mixer size
10. a patch the cows graze in a day

### Worksheet: Level 2 Sample Answer Key

True or False?

1.  False, any object only has 1 possible volume.

Tasks involve multiple steps of calculation. Advanced mathematical techniques may be required.

Measurement math connections for trades & technology

Volume or space is a 3-D or 3 dimensional concept. It always implies Length, Width and Height that a 3-D object or space has. Only objects have volume or take up space. Solid objects have 1 Volume, hollow objects have 2: a bigger outside and a smaller inside Volume/space, depending on wall thickness of the object. Filling a hollow space can be partial or full.

Volume can be measured in Metric or Imperial units, many of these are used only in specific industries. For example grain harvest size in bushels is mostly applicable to grain storage and transport. Volume of wood in trees or logs measured in cords or board feet only relates to logging and lumber production. Space inside a combustion chamber of an engine in cubic inches is only used in automotive parts context. Suitcase, bag and garment sizes and suitability for air travel is concern for manufacturing industry.

Some volume units of measure are funny or anecdotal, they work unofficially as figures of speech. “A 10-gallon hat” relates to volume, so does “a sinkhole the size of 5 Olympic swimming pools”. It could be meaningfully used to indicate Volume during rescue or evacuation.