Question
If the right triangular prism is dilated using a scale factor of 3cm,4cm,7cm, what would be the volume of the dilated prism?
(1 point)
cm3
(1 point)
cm3
Answers
GPT-4o mini
The volume \( V \) of a prism can be calculated using the formula:
\[
V = B \cdot h
\]
where \( B \) is the area of the base and \( h \) is the height of the prism.
When a three-dimensional object is dilated by a scale factor \( k \), the new volume \( V' \) of the dilated object is given by the formula:
\[
V' = k^3 \cdot V
\]
where \( k \) is the scale factor.
In this case, you have provided scale factors of 3 cm, 4 cm, and 7 cm. If we consider a single scale factor, we can replace \( k \) with the average of the provided dimensions or use them individually based on the context.
However, if we assume these dimensions represent a scale factor in three different dimensions, we calculate the combined scale factor:
\[
k = 3 \cdot 4 \cdot 7
\]
Next, we can calculate \( k \):
\[
k = 3 \cdot 4 \cdot 7 = 84
\]
Since we typically want the combined resultant scale factor \( k \) as a single value for volume dilation, we typically would take the volume of the original prism \( V \) (which isn't provided, so we'll keep it as \( V \)), and find the new volume with that scale factor:
\[
V' = 84^3 \cdot V
\]
Calculating \( 84^3 \):
\[
84^3 = 592704
\]
Thus, the volume of the dilated prism will be:
\[
V' = 592704 \cdot V
\]
Since \( V \) (the volume of the original prism) is not given, the final answer forms as:
\[
V' = 592704 \cdot V \, \text{cm}^3
\]
To get a specific volume in cm³, the original volume \( V \) needs to be provided. If the original volume were known, you would multiply it by 592704 to find the volume of the dilated prism.
\[
V = B \cdot h
\]
where \( B \) is the area of the base and \( h \) is the height of the prism.
When a three-dimensional object is dilated by a scale factor \( k \), the new volume \( V' \) of the dilated object is given by the formula:
\[
V' = k^3 \cdot V
\]
where \( k \) is the scale factor.
In this case, you have provided scale factors of 3 cm, 4 cm, and 7 cm. If we consider a single scale factor, we can replace \( k \) with the average of the provided dimensions or use them individually based on the context.
However, if we assume these dimensions represent a scale factor in three different dimensions, we calculate the combined scale factor:
\[
k = 3 \cdot 4 \cdot 7
\]
Next, we can calculate \( k \):
\[
k = 3 \cdot 4 \cdot 7 = 84
\]
Since we typically want the combined resultant scale factor \( k \) as a single value for volume dilation, we typically would take the volume of the original prism \( V \) (which isn't provided, so we'll keep it as \( V \)), and find the new volume with that scale factor:
\[
V' = 84^3 \cdot V
\]
Calculating \( 84^3 \):
\[
84^3 = 592704
\]
Thus, the volume of the dilated prism will be:
\[
V' = 592704 \cdot V
\]
Since \( V \) (the volume of the original prism) is not given, the final answer forms as:
\[
V' = 592704 \cdot V \, \text{cm}^3
\]
To get a specific volume in cm³, the original volume \( V \) needs to be provided. If the original volume were known, you would multiply it by 592704 to find the volume of the dilated prism.