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Calculating the Volume
of a Rectangular Prism
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1. Our Training Videos
Skills Application: Calculating the Volume of a Rectangular Prism
Step-by-Step: Calculating the Volume of a Rectangular Prism
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2. Running with Pi

## Tagged in

Your deep freezer is a rectangular prism and has a fixed interior volume. The space inside the freezer is shared between the volume of food and the volume of air. Cooling depends on the unit's ability to circulate the volume of cold air around food. When the freezer is over stuffed; the air can't circulate and the freezer will run continuously to try to remove the heat.

Keep this mind when you’re packing the freezer with a load of fresh fish, meat or poultry. It is imperative that you leave space for the air to circulate. If you don’t, the center of the pile can remain unfrozen for a long, long time and will start to rot before it freezes. The result is your Sunday dinner being contaminated with food poisoning.

## Running with Pi

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3. Our Training Worksheets

VOLUME OF A RECTANGULAR PRISM

A rectangular prism is a box-shaped object with six sides. Some of the examples in real life are: a mail box, a shoe box, a juice box etc.

V = LWH

Example:
Calculate the volume of a rectangular prism that measures 6 feet long, 3 feet wide and 2 feet high.

V = LWH = 6×3×2 = 36

The volume of the rectangular prism is 36 ft3

In your trades books the word “altitude” (A) may be used instead of height (H).

The formula then looks like this:

V = LWA

The problem with altitude (A) is that the word “area” is also abbreviated as (A)

To avoid confusion, the word altitude is not used on this site, only in aviation context.

VOLUME OF A CUBE
V = s3

Example:
Calculate the volume of a cube that measures 7 cm.

V = s3 = 73 = 343

The volume of the cube is 343 cm3

Check out the ADVANCED tab. The ideas will further your understanding and help with building a bigger mental picture. It builds links between words, numbers and algebra. It is important to cross-link the concepts of volume with many workplace tasks.

### A Short Review

Volume of a rectangular prism is calculated by multiplying its Length by its Width and by its Height:

V = L · W · H

Depending on where a rectangular prism is, Length, Width or Height may be replaced by 3 other measurements. The Volume of wood contained in a maple shelf is better described by the words Thickness, Width and Depth. (See the Advanced tab for more examples and explanation)

V = Th · W · D

Regardless of the words used, the math stays the same: multiply 3 numbers to get a forth.

Rectangular prisms are often found as parts of complex shapes:

• a house is basically a rectangular prism with a triangular prism on top of it,
• a table is slab of a rectangular prism with 4 other rectangular prisms as legs,
• a book can be thought of as a rectangular prism made of a series of bound thin rectangular prisms (pages).

Look for rectangular prisms in objects.

### 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

Example:

Match the numbers in the picture with the corresponding dimensions on the right and fill in the amounts:

Width: _____

Length: _____

Height: _____

Further Example:

Doors dont have a Length. What measurement words describe a doors dimensions that can be used for calculating the Volume of wood used in it?

### Worksheet: Level 1 Answer Key

Width:  7.5 ft

Length:  15.00 ft

Height:  7.5 ft

Volume:  843.75 ft³

### Worksheet: Level 2

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

### Worksheet: Level 2 Sample Questions

Example:

1. Calculate volume if length = 4, width = 3 and height = 2

Further example:

Calculate the Volume of a 3 ½ inch x 15 ¾ x 5 ¼ inch rectangular prism. Name the resultant unit of measure.

### Worksheet: Level 2 Sample Answer Key

L × w × h = V

length × width × height = volume

1.  4 × 3 × 2 = 24

### Worksheet: Level 3

Tasks require a combination of operations. Several steps of calculation are required.

### Worksheet: Level 3 Sample Questions

Calculate the following. Answer in decimals.

Example:

1.  What is the volume of a shipping container in in3, w = 9 ft, L = 20ft, h = 7ft?

Further example:

Whats the Volume of a letter-size sheet of paper? Answer in [in3].

### Worksheet: Level 3 Sample Answer Key

L × w × h = V
length × width × height = volume

1. 20 ft × 9ft × 7ft = 1260 ft³ x 1728 = 2,177,280 in3

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

### Additional Information: Another Way To Get The Answer

Calculate the volume of a room if the height is 3 m, width is 4 m and length is 5 m.

Layout your calculations neatly, so you can review, track changes, correct or learn from them. One way a layout can look is like this:

One way to get the answer:

The room featured in this calculation is a math shape called a rectangular prism. Air conditioning and heating duct segments could be rectangular prisms as well as concrete footings, foundation walls, slabs, beams, bridge decks are all rectangular prisms.

Filing cabinets, drawer capacity, freezers, fridges or rooms are close to being rectangular prisms, not counting the volume of mouldings, handles, hinges etc. The space a threshold takes up or the little extra space in brick work around a chimney flue cleanout are impractical to consider for most trade calculations.

1. Some items are not described with the words height, width and length. If youre looking at the volume of dirt in a trench to be removed, youre describing the trench with the words length, width and DEPTH. Trenches dont have heights. How does that affect volume calculation? Is a trench still a rectangular prism? (trench with vertical walls, square corners)
2. The size of a TetraPack juice box (close enough to perfect rectangular prism) filled with apple juice on a store shelf is described with the words height, a width and depth. Juice boxes dont have lengths.  How does that affect volume calculation?
3. Now envision the juice box as is being made, folded out of paper, and is lying flat on a bench, cut and being glued. As a flattened out template, height becomes length. How does that affect volume calculation?

Hardwood prices are set per volume of lumber, measured in board feet of lumber. Lumber has length, width and THICKNESS. Lumber does not have depth or height. Until it is used as a deck post. Then its length becomes height.

Unlike wood, wire and sheet metal thickness is called gauge. Volume of metal is calculated by multiplying width, length and gauge if shaped like a rectangular prism (flat with square corners). Gauge numbers (0 – 36) are not the same as actual size (0.3 – 0.007 inch).

In some context, length, width, height, depth, thickness are interchangeable. Use of these words depend on the frame of reference of the observer. In calculating volume of rectangular prisms, find the 3 quantities that show the size of the object in the 3 dimensions and multiply them together.

Capacity and volume are not interchangeable, but similar terms. Volume relates to space. This space is often filled with air (which is uncompressed and is at room temperature). Capacity relates to an amount of liquid filling up space. An Olympic swimming pool has a volume of 2500 m3 and gets filled with 2,500,000 L of water (capacity).  An empty juice box has a volume, a full juice box is filled to its capacity.