Question
A cylinder has a surface area of 54π cm2 . If it were dilated using a scale factor of 12 , what is the surface area of the new cylinder?(1 point) Responses 27π cm2 27 pi cm squared 6.75π cm2 6 point 7 5 pi cm squared 108π cm2 108 pi cm squared 13.5π cm2
Answers
GPT-4o mini
To find the surface area of the dilated cylinder, we start with the original surface area, which is \(54\pi \, \text{cm}^2\).
When a three-dimensional object (such as a cylinder) is dilated by a scale factor \(k\), the surface area of the dilated object changes by a factor of \(k^2\).
In this case, the scale factor is \(12\). Therefore, the new surface area can be calculated as follows:
\[
\text{New Surface Area} = \text{Original Surface Area} \times k^2
\]
\[
\text{New Surface Area} = 54\pi \, \text{cm}^2 \times 12^2
\]
\[
\text{New Surface Area} = 54\pi \, \text{cm}^2 \times 144
\]
\[
\text{New Surface Area} = 7776\pi \, \text{cm}^2
\]
Thus, the surface area of the new cylinder is **7776π cm²**.
However, none of the answer choices provided include this value. It seems there might be a misunderstanding regarding the scaling, or you may have provided incorrect original surface area or scale factor. Please double-check the question and the provided options.
When a three-dimensional object (such as a cylinder) is dilated by a scale factor \(k\), the surface area of the dilated object changes by a factor of \(k^2\).
In this case, the scale factor is \(12\). Therefore, the new surface area can be calculated as follows:
\[
\text{New Surface Area} = \text{Original Surface Area} \times k^2
\]
\[
\text{New Surface Area} = 54\pi \, \text{cm}^2 \times 12^2
\]
\[
\text{New Surface Area} = 54\pi \, \text{cm}^2 \times 144
\]
\[
\text{New Surface Area} = 7776\pi \, \text{cm}^2
\]
Thus, the surface area of the new cylinder is **7776π cm²**.
However, none of the answer choices provided include this value. It seems there might be a misunderstanding regarding the scaling, or you may have provided incorrect original surface area or scale factor. Please double-check the question and the provided options.