The question asks us to compute the volume of two rectangular prisms.

1. Left Rectangular Prism:

The dimensions are provided as:

• Length = 4 ft
• Width = 2 ft
• Height = 6 ft

The formula for volume is: $\text{Volume} = \text{Length} \times \text{Width} \times \text{Height}$

Substitute the values: $\text{Volume} = 4 \times 2 \times 6 = 48 \, \text{cubic feet}.$

2. Right Rectangular Prism:

The dimensions are provided in terms of $x$:

• Length = $x^2$
• Width = $x$
• Height = $3x$

Using the same volume formula: $\text{Volume} = \text{Length} \times \text{Width} \times \text{Height}$

Substitute the expressions: $\text{Volume} = (x^2) \times x \times (3x) = x^2 \cdot x \cdot 3x = 3x^4 \, \text{cubic units}.$

Final Results:

• Left Prism: $48 \, \text{ft}^3$
• Right Prism: $3x^4 \, \text{units}^3$

Let me know if you’d like further explanation or related examples!

Follow-up Questions:

1. What happens to the volume of the second prism when $x = 2$?
2. How do the units differ for the two prisms (feet vs. units)?
3. How does the volume of the second prism change as $x$ increases?
4. Can we create a general rule to compare these two prisms at specific values of $x$?
5. How would the formulas differ if one of the dimensions was halved?

Tip:

When dealing with algebraic expressions for volume, simplify step-by-step to avoid errors.