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OO.1 Find the volume

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What is volume?

Volume is the amount of space a three-dimensional object takes up. We measure volume in cubic units.

Examples:
  • The space inside a cardboard box
  • How much water a fish tank can hold
  • The amount of juice in a juice box
Note

Volume is different from area. Area measures flat surfaces (two dimensions), while volume measures space (three dimensions).

Volume of rectangular prisms

To find the volume of a rectangular prism, multiply its length × width × height.

Formula:

Volume = length × width × height

V = l × w × h

Example:

A box is 5 cm long, 3 cm wide, and 2 cm high.

Volume = 5 × 3 × 2 = 30 cubic centimeters (cm³)

Note

All measurements must be in the same units before multiplying. The answer will be in cubic units.

Volume with unit cubes

We can find volume by counting how many unit cubes fit inside a solid shape.

Example:

Imagine a rectangular prism that is 4 cubes long, 3 cubes wide, and 2 cubes high.

To find the total cubes:

  • Bottom layer: 4 × 3 = 12 cubes
  • Two layers: 12 × 2 = 24 cubes

Volume = 24 cubic units

Note

This method helps you understand why we multiply length × width × height to find volume.

Volume of composite figures

Composite figures are made by putting together two or more rectangular prisms.

Steps:
  1. Break the figure into separate rectangular prisms
  2. Find the volume of each prism
  3. Add the volumes together
Example:

An L-shaped bookshelf can be divided into two rectangular prisms:

  • Prism 1: 2 ft × 1 ft × 4 ft = 8 ft³
  • Prism 2: 1 ft × 1 ft × 4 ft = 4 ft³
  • Total volume = 8 + 4 = 12 ft³
Note

When breaking apart composite figures, make sure you don't miss any parts or count any parts twice.

Volume in real world problems

We use volume to solve everyday problems involving space and capacity.

Examples:
  • How much soil is needed to fill a garden planter?
  • How many boxes will fit in a shipping container?
  • How much water does a swimming pool hold?
Sample Problem:

A moving box measures 2 feet by 1.5 feet by 1 foot. What is its volume?

Volume = 2 × 1.5 × 1 = 3 cubic feet

Note

Always read word problems carefully to identify the measurements you need. Draw a picture if it helps!