Question
imagine that a rectangular prism similar to the one shown has a scale factor of 1/2. what is the volume of the new rectangular prism?
a. 60 cm^3
b. 30 cm^3
c. 120 cm^3
d. 15 cm^3
a. 60 cm^3
b. 30 cm^3
c. 120 cm^3
d. 15 cm^3
Answers
GPT-4o mini
To find the volume of a rectangular prism with a scale factor applied, you can use the following formula:
If the scale factor is \( k \) and the original volume is \( V \), then the volume of the new rectangular prism \( V' \) can be calculated using the formula:
\[
V' = k^3 \cdot V
\]
In this case, the scale factor \( k \) is \( \frac{1}{2} \). Therefore, the new volume will be:
\[
V' = \left( \frac{1}{2} \right)^3 \cdot V = \frac{1}{8} \cdot V
\]
To be able to calculate \( V' \), we need the volume of the original prism \( V \). However, since the original volume \( V \) is not provided in the question, we cannot directly calculate the new volume without that information.
If you have the original volume or an option that matches the general form of \( V' = \frac{1}{8} \cdot V \), please provide that value so we can proceed with the calculation. Otherwise, we cannot determine which answer choice (a, b, c, or d) is correct.
If the scale factor is \( k \) and the original volume is \( V \), then the volume of the new rectangular prism \( V' \) can be calculated using the formula:
\[
V' = k^3 \cdot V
\]
In this case, the scale factor \( k \) is \( \frac{1}{2} \). Therefore, the new volume will be:
\[
V' = \left( \frac{1}{2} \right)^3 \cdot V = \frac{1}{8} \cdot V
\]
To be able to calculate \( V' \), we need the volume of the original prism \( V \). However, since the original volume \( V \) is not provided in the question, we cannot directly calculate the new volume without that information.
If you have the original volume or an option that matches the general form of \( V' = \frac{1}{8} \cdot V \), please provide that value so we can proceed with the calculation. Otherwise, we cannot determine which answer choice (a, b, c, or d) is correct.