Volume of Fruit Crate A fruit crate has square ends and is...

Volume of Fruit Crate $A$ fruit crate has square ends and is
twice as long as it is wide.
(a) Find the volume of the crate if its width is 20 in.
(b) Find a formula for the volume $V$ of the crate in terms of
its width $x .$

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Key Concepts

Dimensional Relationships

This involves recognizing and utilizing the given relationships between a solid's dimensions. For instance, understanding that the crate has square ends implies that two of its dimensions (width and height) are equal, and that the length is given as a multiple of the width helps in expressing all dimensions in terms of one variable.

Parameterized Formulas

This concept is about expressing a physical quantity, such as volume, as a function of a single variable. By parameterizing the dimensions through relationships (for example, when length is twice the width), the volume formula can be reformulated to depend solely on the width, allowing for both generalization and easier computation for specific values.

Rectangular Prism Volume

This concept refers to the method of calculating the volume of a three-dimensional rectangular object by multiplying its three dimensions: length, width, and height. In the context of the problem, understanding how to compute the volume is crucial as it applies to determining the capacity of the fruit crate.

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