Question
Imagine that a rectangular prism similar to the one shown has a scale factor of 12
. What is the volume of the new rectangular prism?
(1 point)
Responses
60 cm3
60 cm cubed
15 cm3
15 cm cubed
120 cm3
120 cm cubed
30 cm3
. What is the volume of the new rectangular prism?
(1 point)
Responses
60 cm3
60 cm cubed
15 cm3
15 cm cubed
120 cm3
120 cm cubed
30 cm3
Answers
GPT-4o mini
To determine the volume of the new rectangular prism with a scale factor of 12, we first need to know the volume of the original rectangular prism.
The volume \( V \) of a rectangular prism is calculated using the formula:
\[
V = \text{length} \times \text{width} \times \text{height}
\]
If we denote the volume of the original rectangular prism as \( V_{\text{original}} \), the volume of the new rectangular prism, which is similar to the original one, can be found using the scale factor.
When the dimensions of a three-dimensional shape are scaled by a factor \( k \), the volume scales by \( k^3 \). Therefore, if the scale factor is 12, the volume of the new rectangular prism is:
\[
V_{\text{new}} = V_{\text{original}} \times 12^3
\]
\[
= V_{\text{original}} \times 1728
\]
However, without the volume of the original prism given among the options, we can't calculate the new volume directly. If you can provide the volume of the original rectangular prism, I can help calculate the new volume based on the scale factor.
If the original volume is 1 cm³, for example:
\[
V_{\text{new}} = 1 \times 1728 = 1728 \text{ cm}^3
\]
Please check the options you’ve provided; none of them seem compatible with scaling a volume by 12 (which leads to a much larger value). Could you please confirm the original volume or the context of the problem?
The volume \( V \) of a rectangular prism is calculated using the formula:
\[
V = \text{length} \times \text{width} \times \text{height}
\]
If we denote the volume of the original rectangular prism as \( V_{\text{original}} \), the volume of the new rectangular prism, which is similar to the original one, can be found using the scale factor.
When the dimensions of a three-dimensional shape are scaled by a factor \( k \), the volume scales by \( k^3 \). Therefore, if the scale factor is 12, the volume of the new rectangular prism is:
\[
V_{\text{new}} = V_{\text{original}} \times 12^3
\]
\[
= V_{\text{original}} \times 1728
\]
However, without the volume of the original prism given among the options, we can't calculate the new volume directly. If you can provide the volume of the original rectangular prism, I can help calculate the new volume based on the scale factor.
If the original volume is 1 cm³, for example:
\[
V_{\text{new}} = 1 \times 1728 = 1728 \text{ cm}^3
\]
Please check the options you’ve provided; none of them seem compatible with scaling a volume by 12 (which leads to a much larger value). Could you please confirm the original volume or the context of the problem?