If the right triangular prism is dilated using a scale factor of 4, what would the volume of the dilated prism be?

Question

(1 point)
volume =

Answer 1

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.

Answer 2

w=4,l=7,h=3

Answer 3

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.