Question
Determine the volume of the rectangular prism if it were dilated using a scale factor of 4. (1 point) Responses 6 m3 6 m cubed 1,536 m3 1,536 m cubed 96 m3 96 m cubed 384 m3
Answers
Answered by
GPT-4o mini
To determine the volume of the rectangular prism after dilation using a scale factor of 4, we need to follow these steps:
1. **Understand the effect of dilation on volume**: When a three-dimensional shape is dilated by a scale factor \( k \), the volume of the shape increases by a factor of \( k^3 \). For a scale factor of 4, the volume will increase by \( 4^3 = 64 \).
2. **Calculate the new volume**: If we denote the original volume of the prism as \( V \), the new volume after dilation will be:
\[
V_{\text{new}} = V \times 64
\]
3. **Select the original volume**: However, the original volume of the rectangular prism is not provided in the question. To find the new volume after dilation, we will need the original volume \( V \).
Since we don't have the original volume, let's look at the provided options and determine which one could be the volume after dilation.
- If \( V_{\text{new}} = 6 \, \text{m}^3 \), \( V = 6/64 \approx 0.09375 \, \text{m}^3 \)
- If \( V_{\text{new}} = 1,536 \, \text{m}^3 \), \( V = 1,536/64 = 24 \, \text{m}^3 \)
- If \( V_{\text{new}} = 96 \, \text{m}^3 \), \( V = 96/64 = 1.5 \, \text{m}^3 \)
- If \( V_{\text{new}} = 384 \, \text{m}^3 \), \( V = 384/64 = 6 \, \text{m}^3 \)
To find the new volume after dilating the rectangular prism by a scale factor of 4, if I assume that the original volume of \( 24 \, \text{m}^3 \) is a plausible option (yielding first available option), I would mark \( 1,536 \, \text{m}^3 \) as the collision result.
Thus, if \( V \) were \( 24 \, \text{m}^3 \):
\[
V_{\text{new}} = 24 \times 64 = 1,536 \, \text{m}^3
\]
Therefore, the answer is:
**1,536 m³ or 1,536 m cubed**.
1. **Understand the effect of dilation on volume**: When a three-dimensional shape is dilated by a scale factor \( k \), the volume of the shape increases by a factor of \( k^3 \). For a scale factor of 4, the volume will increase by \( 4^3 = 64 \).
2. **Calculate the new volume**: If we denote the original volume of the prism as \( V \), the new volume after dilation will be:
\[
V_{\text{new}} = V \times 64
\]
3. **Select the original volume**: However, the original volume of the rectangular prism is not provided in the question. To find the new volume after dilation, we will need the original volume \( V \).
Since we don't have the original volume, let's look at the provided options and determine which one could be the volume after dilation.
- If \( V_{\text{new}} = 6 \, \text{m}^3 \), \( V = 6/64 \approx 0.09375 \, \text{m}^3 \)
- If \( V_{\text{new}} = 1,536 \, \text{m}^3 \), \( V = 1,536/64 = 24 \, \text{m}^3 \)
- If \( V_{\text{new}} = 96 \, \text{m}^3 \), \( V = 96/64 = 1.5 \, \text{m}^3 \)
- If \( V_{\text{new}} = 384 \, \text{m}^3 \), \( V = 384/64 = 6 \, \text{m}^3 \)
To find the new volume after dilating the rectangular prism by a scale factor of 4, if I assume that the original volume of \( 24 \, \text{m}^3 \) is a plausible option (yielding first available option), I would mark \( 1,536 \, \text{m}^3 \) as the collision result.
Thus, if \( V \) were \( 24 \, \text{m}^3 \):
\[
V_{\text{new}} = 24 \times 64 = 1,536 \, \text{m}^3
\]
Therefore, the answer is:
**1,536 m³ or 1,536 m cubed**.