Volume

Definition

Volume is the measure of the amount of space an object occupies, typically in three dimensions. It is often measured in cubic units such as cubic meters or cubic feet.

5 Must Know Facts For Your Next Test

1. The volume of a rectangular prism can be calculated using the formula $V = l \cdot w \cdot h$ where $l$, $w$, and $h$ are the length, width, and height respectively.
2. For a cylinder, the volume is given by $V = \pi r^2 h$ where $r$ is the radius of the base and $h$ is the height.
3. The volume of a sphere is calculated using $V = \frac{4}{3} \pi r^3$ where $r$ is the radius.
4. In algebraic models, volume can often be expressed as polynomial equations involving dimensions.
5. Understanding how to solve inequalities involving volumes can help in solving real-world problems like determining capacity constraints.

Review Questions

• How do you calculate the volume of a rectangular prism?
• What is the formula for finding the volume of a cylinder?
• How can inequalities involving volumes be applied to real-world problems?

Related terms

Surface Area: The total area that covers the surface of a three-dimensional object.

Polynomial Equation: An equation involving terms with variables raised to whole number exponents.

Inequality:

A mathematical statement that shows the relationship between expressions that are not equal, using symbols like >, <, ≥, or ≤.