A certain chest (a rectangular prism) has the following dimensions: 1.5 feet wide, 2.5 feet long, and 2 feet deep. If the chest currently holds 3 blankets that individually occupy 1 cubic foot each, then how much additional space is available in the chest? \(\mathrm{ft}^3\)

Understanding the volume of a rectangular prism is essential in solving a variety of real-world problems, from packing for a move to designing objects. Simply put, the volume of a rectangular prism is the amount of space inside it, which can be found using the formula:
\( V = l \times w \times h \)
where \( l \) is the length, \( w \) is the width, and \( h \) is the height of the prism. All measurements must be in the same unit, and the volume will be in cubic units, such as cubic feet (\(\text{ft}^3\)). In the given problem, we apply this simple yet powerful formula to find the available space inside a chest.

Real-World Application

When determining how much you can fit into a space, like packing a storage box or filling a shipping container, calculating the volume of the container is the first step. This knowledge is not only crucial for those facing GED math problems but also for anyone needing to maximize space efficiency.

The General Educational Development (GED) test covers four subjects, one of which is Mathematical Reasoning. This section challenges test-takers on various topics, including arithmetic, algebra, geometry, and data analysis.
Understanding how to calculate volume is often vital for GED math problems, where practical questions similar to the example given—determining the space within a chest—may appear. To tackle GED math problems effectively, it's important to have a clear grasp on formulas and mathematical concepts, practice problem-solving, and develop a methodical approach to breaking down questions into manageable steps, as seen in our exercise solution.

Study Tips

• Memorize key formulas, like the one for the volume of a rectangular prism.
• Understand the units used for measurement and how to convert between them if necessary.
• Break down complex problems into smaller, more manageable steps.

Consistent practice with exercises like this promotes a deeper understanding and prepares students for the types of questions they may face on the GED exam.

Subtracting volumes is a process used to determine the available or remaining space when part of the space is already occupied. As shown in the exercise, after calculating the volume of the chest, we found that the blankets occupied some of that volume. To find the unoccupied space, we subtracted the volume of the blankets from the total volume of the chest.
The formula for the subtraction of volumes in this context is:
\( V_{remaining} = V_{total} - V_{occupied} \)
It's important to note that the volumes must be in the same units when performing the subtraction. This skill is essential in real-life scenarios like loading cargo, where you need to determine how much more can fit or in construction when calculating the volume of the material needed to fill a space.

Practical Example

Imagine filling a garden bed with soil. If some of the volume is already taken up by plants or decorations, you would need to subtract that occupied volume from the total volume of the garden bed to know how much soil you'll need to add—the same principle we've applied in our textbook exercise.