Question

The volume of a rectangular box is 3x(3x + 4)
(3x - 1). (Drawing is not to scale.)
Height 3x - 1
Length 3x + 4
Width 3x
Which statement about the volume of the box is true?
O The volume does not depend on the width,
3х.
• The volume is the sum of the length, 3x + 4, the width, 3x, and the height, 3x - 1.
• The volume is the product of the area of the base, 3x(3x + 4), and the height, 3x - 1.
O The volume is the product of the length,
3x + 4, and the width, 3x.

Answer 1

To analyze the volume of the rectangular box described, we can use the formulas for the volume of a box. The volume \( V \) of a rectangular box can be expressed as:

\[
V = \text{length} \times \text{width} \times \text{height}
\]

In this case, the dimensions of the box are given as:
- Height = \( 3x - 1 \)
- Length = \( 3x + 4 \)
- Width = \( 3x \)

Thus, the volume \( V \) can be calculated as follows:

\[
V = (3x + 4) \times (3x) \times (3x - 1)
\]

From this expression, we can consider the statements provided:

1. **The volume does not depend on the width, 3x.**
**False.** The volume does depend on the width since it is one of the factors in the volume calculation.

2. **The volume is the sum of the length, 3x + 4, the width, 3x, and the height, 3x - 1.**
**False.** The volume is not the sum; it is the product of the dimensions.

3. **The volume is the product of the area of the base, 3x(3x + 4), and the height, 3x - 1.**
**True.** The area of the base is \( \text{width} \times \text{length} = 3x \times (3x + 4) \), and the volume can be expressed as:
\[
V = \text{Area of base} \times \text{height} = (3x(3x + 4))(3x - 1)
\]

4. **The volume is the product of the length, 3x + 4, and the width, 3x.**
**False.** This expression does not account for the height of the box; just the length and width are used.

Therefore, the correct statement about the volume of the box is:

- **The volume is the product of the area of the base, \( 3x(3x + 4) \), and the height, \( 3x - 1 \).**