Question
If the right triangular prism is dilated using a scale factor of 4, what would the volume of the dilated prism be?
(1 point)
volume =
Answers
GPT-4o mini
To find the volume of a dilated right triangular prism, you can use the fact that when an object is dilated by a scale factor \(k\), its volume changes by a factor of \(k^3\).
If the scale factor is 4, then the volume of the dilated prism will be:
\[
\text{Volume}_{\text{dilated}} = k^3 \times \text{Volume}_{\text{original}}
\]
Substituting the scale factor:
\[
\text{Volume}_{\text{dilated}} = 4^3 \times \text{Volume}_{\text{original}} = 64 \times \text{Volume}_{\text{original}}
\]
Therefore, the volume of the dilated prism will be 64 times the volume of the original prism. To provide a specific numerical answer, you would need the volume of the original prism.
If the scale factor is 4, then the volume of the dilated prism will be:
\[
\text{Volume}_{\text{dilated}} = k^3 \times \text{Volume}_{\text{original}}
\]
Substituting the scale factor:
\[
\text{Volume}_{\text{dilated}} = 4^3 \times \text{Volume}_{\text{original}} = 64 \times \text{Volume}_{\text{original}}
\]
Therefore, the volume of the dilated prism will be 64 times the volume of the original prism. To provide a specific numerical answer, you would need the volume of the original prism.
w=4,l=7,h=3
GPT-4o mini
To calculate the volume of the original right triangular prism, you can use the formula for the volume of a prism:
\[
\text{Volume} = \text{Base Area} \times \text{Height}
\]
For a right triangular prism, the base area (which is a right triangle) can be calculated as:
\[
\text{Base Area} = \frac{1}{2} \times \text{width} \times \text{length}
\]
Given dimensions:
- Width (w) = 4
- Length (l) = 7
- Height (h) = 3
### Step 1: Calculate the base area
\[
\text{Base Area} = \frac{1}{2} \times 4 \times 7 = \frac{28}{2} = 14
\]
### Step 2: Calculate the volume of the original prism
\[
\text{Volume}_{\text{original}} = \text{Base Area} \times \text{Height} = 14 \times 3 = 42
\]
### Step 3: Calculate the volume of the dilated prism
Using the dilation scale factor of 4:
\[
\text{Volume}_{\text{dilated}} = 64 \times \text{Volume}_{\text{original}} = 64 \times 42
\]
### Step 4: Compute the final volume
\[
\text{Volume}_{\text{dilated}} = 64 \times 42 = 2688
\]
Thus, the volume of the dilated prism is **2688 cubic units**.
\[
\text{Volume} = \text{Base Area} \times \text{Height}
\]
For a right triangular prism, the base area (which is a right triangle) can be calculated as:
\[
\text{Base Area} = \frac{1}{2} \times \text{width} \times \text{length}
\]
Given dimensions:
- Width (w) = 4
- Length (l) = 7
- Height (h) = 3
### Step 1: Calculate the base area
\[
\text{Base Area} = \frac{1}{2} \times 4 \times 7 = \frac{28}{2} = 14
\]
### Step 2: Calculate the volume of the original prism
\[
\text{Volume}_{\text{original}} = \text{Base Area} \times \text{Height} = 14 \times 3 = 42
\]
### Step 3: Calculate the volume of the dilated prism
Using the dilation scale factor of 4:
\[
\text{Volume}_{\text{dilated}} = 64 \times \text{Volume}_{\text{original}} = 64 \times 42
\]
### Step 4: Compute the final volume
\[
\text{Volume}_{\text{dilated}} = 64 \times 42 = 2688
\]
Thus, the volume of the dilated prism is **2688 cubic units**.