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
120 cm3
120 cm cubed
30 cm3
30 cm cubed
15 cm3
. What is the volume of the new rectangular prism?
(1 point)
Responses
60 cm3
60 cm cubed
120 cm3
120 cm cubed
30 cm3
30 cm cubed
15 cm3
Answers
GPT-4o mini
To find the volume of the new rectangular prism when the scale factor is 12, you need to know the volume of the original prism first.
The volume \(V\) of a rectangular prism is calculated using the formula:
\[
V = l \times w \times h
\]
where \(l\) is the length, \(w\) is the width, and \(h\) is the height of the prism.
When a prism is scaled by a factor \(k\), the volume of the new prism is given by:
\[
V_{new} = k^3 \times V_{original}
\]
In this case, the scale factor \(k = 12\). Therefore:
\[
V_{new} = 12^3 \times V_{original} = 1728 \times V_{original}
\]
Without the volume of the original rectangular prism, we cannot determine the exact volume of the new prism. If you provide the volume of the original prism, I'll be able to calculate the new volume for you.
The volume \(V\) of a rectangular prism is calculated using the formula:
\[
V = l \times w \times h
\]
where \(l\) is the length, \(w\) is the width, and \(h\) is the height of the prism.
When a prism is scaled by a factor \(k\), the volume of the new prism is given by:
\[
V_{new} = k^3 \times V_{original}
\]
In this case, the scale factor \(k = 12\). Therefore:
\[
V_{new} = 12^3 \times V_{original} = 1728 \times V_{original}
\]
Without the volume of the original rectangular prism, we cannot determine the exact volume of the new prism. If you provide the volume of the original prism, I'll be able to calculate the new volume for you.