Question
If the right triangular prism is dilated using a scale factor of 3, what would be the volume of the dilated prism? (1 point) 3cm 4 cm 7 cm
cm3
cm3
Answers
Answered by
GPT-4o mini
To find the volume of the dilated right triangular prism, we first need to know the volume of the original prism before dilation. The volume \( V \) of a prism is calculated as follows:
\[
V = \text{Base Area} \times \text{Height}
\]
When a shape is dilated by a scale factor, the volume changes by the cube of that scale factor. For a scale factor \( k \), the new volume \( V' \) after dilation is given by:
\[
V' = k^3 \times V
\]
In this case, the scale factor is \( k = 3 \), so we calculate:
\[
k^3 = 3^3 = 27
\]
This means that the volume of the dilated prism will be 27 times the volume of the original prism. However, without knowing the volume of the original prism, we cannot calculate the exact volume of the dilated prism.
If you have the volume of the original prism, you can multiply it by 27 to find the volume of the dilated prism. If the original volume is not provided, we cannot determine the volume of the dilated prism.
Please provide the volume of the original prism if you have it!
\[
V = \text{Base Area} \times \text{Height}
\]
When a shape is dilated by a scale factor, the volume changes by the cube of that scale factor. For a scale factor \( k \), the new volume \( V' \) after dilation is given by:
\[
V' = k^3 \times V
\]
In this case, the scale factor is \( k = 3 \), so we calculate:
\[
k^3 = 3^3 = 27
\]
This means that the volume of the dilated prism will be 27 times the volume of the original prism. However, without knowing the volume of the original prism, we cannot calculate the exact volume of the dilated prism.
If you have the volume of the original prism, you can multiply it by 27 to find the volume of the dilated prism. If the original volume is not provided, we cannot determine the volume of the dilated prism.
Please provide the volume of the original prism if you have it!