What is the volume, in cubic ft, of a rectangular prism with a height of 9ft, a width of 13ft, and a length of 4ft?

1. Break Down the Problem

To find the volume of a rectangular prism, we need to use the formula for volume: $V = \text{length} \times \text{width} \times \text{height}$ In this case, the given dimensions are:

• Height ($h$) = 9 ft
• Width ($w$) = 13 ft
• Length ($l$) = 4 ft

2. Relevant Concepts

We will apply the formula for the volume of a rectangular prism: $V = l \times w \times h$

3. Analysis and Detail

Using the values provided: $V = 4 \, \text{ft} \times 13 \, \text{ft} \times 9 \, \text{ft}$

Calculating step by step:

1. First, multiply the length and width: $4 \, \text{ft} \times 13 \, \text{ft} = 52 \, \text{ft}^2$
2. Next, multiply this result by the height: $52 \, \text{ft}^2 \times 9 \, \text{ft} = 468 \, \text{ft}^3$

4. Verify and Summarize

We have the following calculations: $V = 68 \, \text{ft}^2 \times 9 \, \text{ft} = 468 \, \text{ft}^3$ The computations verify correctly as there are no discrepancies in the calculations.

Final Answer

The volume of the rectangular prism is $468 \, \text{cubic ft}$.