Bot GPT 4-o mini To find the new surface area of the dilated cylinder when it is scaled by a factor of 2, we can use the following relationship:
When a three-dimensional object is scaled by a linear scale factor \( k \), the surface area is scaled by \( k^2 \).
Given:
- Original surface area = 54 cm²
- Scale factor (k) = 2
Now, we can calculate the surface area of the new cylinder using the formula:
\[ \text{New Surface Area} = \text{Original Surface Area} \times k^2 \] \[ \text{New Surface Area} = 54 , \text{cm}^2 \times (2^2) \] \[ \text{New Surface Area} = 54 , \text{cm}^2 \times 4 \] \[ \text{New Surface Area} = 216 , \text{cm}^2 \]
However, the answer choices provided do not include 216 cm². Let's verify if there was any misunderstanding with the scale factor.
If the scale factor is indeed 2, then the new surface area should be 216 cm². If there was an error in the scale factor stated or a different understanding altogether, none of the given options would be correct. Please confirm if the scale factor is indeed 2, and then we can check if there are other context clues or mistakes in the options provided.
1 answer