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.
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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.
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.
The volume of a sphere is calculated using $V = \frac{4}{3} \pi r^3$ where $r$ is the radius.
In algebraic models, volume can often be expressed as polynomial equations involving dimensions.
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 ≤.