Problem 73 - Elementary Algebra

Question

The interior of an industrial freezer measures 3 feet wide by 3 feet deep and 4 feet high. What is the volume of the freezer?

Step-by-Step Solution

Answer

The volume is 36 cubic feet.

Step 1: Understand the Problem

We are given the dimensions of an industrial freezer: 3 feet wide, 3 feet deep, and 4 feet high. We need to calculate the volume of the freezer, which refers to the amount of space inside it.

Step 2: Recall the Volume Formula for a Rectangular Prism

The formula for finding the volume of a rectangular prism is to multiply its length (or width), depth (or breadth), and height. The volume formula is: \[V = ext{width} imes ext{depth} imes ext{height}\]

Step 3: Substitute the Given Values

Insert the given measurements into the volume formula: \[V = 3 ext{ feet (width)} imes 3 ext{ feet (depth)} imes 4 ext{ feet (height)}\]

Step 4: Calculate the Volume

Perform the multiplication to find the volume: \[V = 3 imes 3 imes 4 = 36 ext{ cubic feet}\]

Step 5: Interpret the Result

The volume of the industrial freezer is 36 cubic feet, which means it can hold 36 cubic feet of material.

Key Concepts

Rectangular Prism

A rectangular prism is a 3-dimensional shape which has six faces, all of which are rectangles. It looks like a box or a brick, and it’s very common in real-world objects like bookshelves, boxes, and freezers. The key characteristics of a rectangular prism are:

• Length, Width, and Height: These are the three dimensions of the prism. They define its size in space.
• Right Angles: All corner angles are right angles, meaning each face meets its adjacent faces at a 90-degree angle.
• Opposite Faces: Each pair of opposite faces is congruent, meaning they are identical in size and shape.

Understanding a rectangular prism's structure is crucial for calculating its volume and solving related problems. Each dimension plays a role in determining the prism's capacity.

Volume Calculation

The volume of a rectangular prism represents the amount of space it occupies. It’s measured in cubic units and tells us how much material can fit inside. To find the volume, you use this essential formula:

• Multiply the length (or width), breadth (or depth), and height.

In our freezer example, the given dimensions are 3 feet wide, 3 feet deep, and 4 feet high. So, using the formula:\[ V = \text{width} \times \text{depth} \times \text{height} \]
We substitute the values:\[ V = 3 \times 3 \times 4 \]
This calculation gives us:\[ V = 36 \text{ cubic feet} \]This means the freezer can contain 36 cubic feet of material. Volume calculations are essential in everyday tasks, including packing, construction, and storage.

Mathematical Problem Solving

Mathematical problem solving involves understanding the problem and applying appropriate strategies to find a solution. Let’s break it down using our example:

• Understanding the Problem: Identify what is asked—in this case, the volume of the freezer.
• Select the Correct Formula: Use the volume formula for a rectangular prism, as we know it involves multiplying the dimensions.
• Substitute Known Values: Carefully insert the given dimensions into the formula.
  
• Perform Calculations: Multiply the values correctly. This step needs attention to detail to avoid mistakes.
  
• Interpret the Result: Think about what the result means—a clearer understanding is that the freezer’s space holds 36 cubic feet of material.

By following these methods, anyone can solve similar mathematical problems with confidence. Problem-solving increases logical thinking and precision, which are valuable skills in daily life.