Question
The volume of the rectangular box is 3x(3x+4)(3x-1)
Which statement about the volume of the box is true?
The volume the product of the length, 3x+4, the width, 3x
The volume of the product of the area of the case, 3x(3x+4), and the high, 3x-1
The volume is the sum of the length, 3x+4, the width, 3x, and the height, 3x-1
The volume does not depend on the width, 3x
Which statement about the volume of the box is true?
The volume the product of the length, 3x+4, the width, 3x
The volume of the product of the area of the case, 3x(3x+4), and the high, 3x-1
The volume is the sum of the length, 3x+4, the width, 3x, and the height, 3x-1
The volume does not depend on the width, 3x
Answers
Answered by
GPT-4o mini
To analyze the given volume of the rectangular box, which is expressed as \( V = 3x(3x + 4)(3x - 1) \), we can evaluate each statement one by one.
1. **The volume is the product of the length, \( 3x + 4 \), and the width, \( 3x \)**:
- This is not true, since the volume also includes height (which is \( 3x - 1 \) in this case). The correct statement would include the height.
2. **The volume is the product of the area of the base, \( 3x(3x + 4) \), and the height, \( 3x - 1 \)**:
- This statement is true. The area of the base can be expressed as \( \text{Base Area} = \text{Length} \times \text{Width} = (3x + 4)(3x) = 3x(3x + 4) \). The volume then is the base area times the height:
\[
V = \text{Base Area} \times \text{Height} = 3x(3x + 4)(3x - 1)
\]
3. **The volume is the sum of the length, \( 3x + 4 \), the width, \( 3x \), and the height, \( 3x - 1 \)**:
- This is false because the volume is not the sum of length, width, and height; it is the product of these dimensions.
4. **The volume does not depend on the width, \( 3x \)**:
- This statement is also false, as the volume clearly depends on the width \( 3x \) as it is one of the factors in the multiplication that defines the volume.
Based on the analysis, the second statement is the correct one. Therefore, the true statement is:
**The volume is the product of the area of the base, \( 3x(3x + 4) \), and the height, \( 3x - 1 \).**
1. **The volume is the product of the length, \( 3x + 4 \), and the width, \( 3x \)**:
- This is not true, since the volume also includes height (which is \( 3x - 1 \) in this case). The correct statement would include the height.
2. **The volume is the product of the area of the base, \( 3x(3x + 4) \), and the height, \( 3x - 1 \)**:
- This statement is true. The area of the base can be expressed as \( \text{Base Area} = \text{Length} \times \text{Width} = (3x + 4)(3x) = 3x(3x + 4) \). The volume then is the base area times the height:
\[
V = \text{Base Area} \times \text{Height} = 3x(3x + 4)(3x - 1)
\]
3. **The volume is the sum of the length, \( 3x + 4 \), the width, \( 3x \), and the height, \( 3x - 1 \)**:
- This is false because the volume is not the sum of length, width, and height; it is the product of these dimensions.
4. **The volume does not depend on the width, \( 3x \)**:
- This statement is also false, as the volume clearly depends on the width \( 3x \) as it is one of the factors in the multiplication that defines the volume.
Based on the analysis, the second statement is the correct one. Therefore, the true statement is:
**The volume is the product of the area of the base, \( 3x(3x + 4) \), and the height, \( 3x - 1 \).**
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