Answer :
To solve this problem, we need to interpret the notation \( V(3) = 27 \) correctly. Let's break down the function notation and the interpretation step by step.
1. Understanding the Volume Function:
- The volume of a cube \( V \) depends on the side length \( s \).
- The formula for the volume of a cube is \( V = s^3 \).
2. Interpreting \( V(3) \):
- Here, \( V(3) \) means the volume when the side length of the cube is \( 3 \) feet.
- Using the formula, if \( s = 3 \) feet, then \( V = 3^3 = 27 \) cubic feet.
3. Analyzing the Given Statement \( V(3) = 27 \):
- This equation tells us that when the side length of a cube is 3 feet, the volume of the cube is 27 cubic feet.
4. Evaluating the Answer Choices:
- A. A cube with a volume of 3 cubic feet has side lengths of 27 feet.
- Incorrect. \( V(3) \) specifically gives us the volume of a cube with side length 3 feet, not the other way around.
- B. A cube with side lengths of 3 feet has a volume of 27 cubic feet.
- Correct. This matches our interpretation that \( V(3) = 27 \) means the side length is 3 feet and the volume is 27 cubic feet.
- C. Three sides of the cube have a total length of 27 feet.
- Incorrect. The cube has side length 3 feet, making three sides a total of \( 3 + 3 + 3 = 9 \) feet.
- D. Three of these cubes will have a total volume of 27 cubic feet.
- Incorrect. Three cubes each with volume 27 cubic feet will have a total volume of \( 3 \times 27 = 81 \) cubic feet.
5. Conclusion:
- The best interpretation of \( V(3) = 27 \) is that a cube with side lengths of 3 feet has a volume of 27 cubic feet.
Hence, the correct answer is B: A cube with side lengths of 3 feet has a volume of 27 cubic feet.
1. Understanding the Volume Function:
- The volume of a cube \( V \) depends on the side length \( s \).
- The formula for the volume of a cube is \( V = s^3 \).
2. Interpreting \( V(3) \):
- Here, \( V(3) \) means the volume when the side length of the cube is \( 3 \) feet.
- Using the formula, if \( s = 3 \) feet, then \( V = 3^3 = 27 \) cubic feet.
3. Analyzing the Given Statement \( V(3) = 27 \):
- This equation tells us that when the side length of a cube is 3 feet, the volume of the cube is 27 cubic feet.
4. Evaluating the Answer Choices:
- A. A cube with a volume of 3 cubic feet has side lengths of 27 feet.
- Incorrect. \( V(3) \) specifically gives us the volume of a cube with side length 3 feet, not the other way around.
- B. A cube with side lengths of 3 feet has a volume of 27 cubic feet.
- Correct. This matches our interpretation that \( V(3) = 27 \) means the side length is 3 feet and the volume is 27 cubic feet.
- C. Three sides of the cube have a total length of 27 feet.
- Incorrect. The cube has side length 3 feet, making three sides a total of \( 3 + 3 + 3 = 9 \) feet.
- D. Three of these cubes will have a total volume of 27 cubic feet.
- Incorrect. Three cubes each with volume 27 cubic feet will have a total volume of \( 3 \times 27 = 81 \) cubic feet.
5. Conclusion:
- The best interpretation of \( V(3) = 27 \) is that a cube with side lengths of 3 feet has a volume of 27 cubic feet.
Hence, the correct answer is B: A cube with side lengths of 3 feet has a volume of 27 cubic feet.
