Volume of Rectangular Prisms

Learn to calculate the volume of boxes and rectangular shapes

What is Volume?

Volume is the amount of space inside a 3-dimensional object.

It's measured in cubic units (like cm³, m³, in³, ft³).

A rectangular prism is a 3D shape with 6 rectangular faces (like a box).

$V = l \times w \times h$

where:

You can also think of it as: $V = (\text{area of base}) \times \text{height}$

A cube is a special rectangular prism where all sides are equal: $V = s^3$

where $s$ = side length

Find the volume of a cube with side length 4 cm.

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Solution:

Use the formula: $V = s^3$

$V = 4^3$ $V = 4 \times 4 \times 4$ $V = 64$

Answer: 64 cm³

A box has dimensions 6 inches long, 4 inches wide, and 5 inches tall. What is its volume?

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Solution:

Use the formula: $V = l \times w \times h$

$V = 6 \times 4 \times 5$ $V = 120$

Answer: 120 cubic inches (or 120 in³)

An aquarium is 30 inches long, 12 inches wide, and 18 inches tall. If it is filled to 2 inches below the top, what is the volume of water?

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Solution:

Water height: $18 - 2 = 16$ inches

Volume of water: $V = l \times w \times h$ $V = 30 \times 12 \times 16$ $V = 5,760$

Answer: 5,760 in³ of water

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