Question
A rectangle prism is dilated using a scale factor of 4. Determine how this will affect the surface area of the prism.
The surface area will be 1/4 the size of the original prism.
The surface area will be 4 times the size of the original prism.
The surface area will be 8 times the size of the original prism.
The surface area will be 16 times the size of the original prism.
The surface area will be 1/4 the size of the original prism.
The surface area will be 4 times the size of the original prism.
The surface area will be 8 times the size of the original prism.
The surface area will be 16 times the size of the original prism.
Answers
GPT-4o mini
When a three-dimensional shape like a rectangular prism is dilated using a scale factor, the surface area is affected by the square of that scale factor.
If the scale factor is \( k \), the new surface area will be \( k^2 \) times the original surface area.
In your case, the scale factor is 4:
\[
\text{Surface area scaling factor} = 4^2 = 16
\]
Thus, the surface area of the dilated prism will be 16 times the size of the original prism.
Therefore, the correct answer is:
**The surface area will be 16 times the size of the original prism.**
If the scale factor is \( k \), the new surface area will be \( k^2 \) times the original surface area.
In your case, the scale factor is 4:
\[
\text{Surface area scaling factor} = 4^2 = 16
\]
Thus, the surface area of the dilated prism will be 16 times the size of the original prism.
Therefore, the correct answer is:
**The surface area will be 16 times the size of the original prism.**