Volume: Prisms, Cylinders, Cones, Spheres

Definition: Volume is the total amount of space inside a three dimensional shape. Volume is measured in cubic units, such as “cubic inches” or in³.

Each three dimensional figure has its own unique volume formula. For example, to find the volume of a rectangular prism, we can multiply the length, the width and the height of the prism together.
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Example: Find the volume of figure:



Determine the appropriate volume formula for this figure and plug in the given values.

Step 1: Identify the figure.

As this figure has a square base and triangular faces, we know it is a square pyramid and can apply the following formula:
Volume = 1/3 * (area of base) * height

Step 2: Plug the given values into the formula.

This figure has a height of 9 cm, and edge lengths of 8 cm. Plugging this information into the formula we get:

Volume = 1/3 * 8² * 9

Step 3: Simplify to find the volume.

V = 1/3 * 8² * 9
V = 1/3 * 64 * 9
V = 1/3 * 576
V = 576 / 3 = 192

Because volume is always measured in cubic units, we will label this answer as:
V = 192 cubic cm or 192 cm³

Check out another example here.

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