To find the new surface area of the cylinder after a dilation with a scale factor of 4, we need to understand how the surface area changes with dilation.
When an object is dilated by a scale factor \( k \), the surface area scales by the factor \( k^2 \). In this case, the scale factor \( k \) is 4, so the surface area will increase by a factor of \( 4^2 = 16 \).
Let \( SA \) be the original surface area of the cylinder. The new surface area \( SA' \) after dilation is given by:
\[ SA' = SA \times k^2 = SA \times 16 \]
Since the original surface area is not provided in the options, we will need to match it with one of the given choices after considering that it must be multiplied by 16.
Now, let's analyze the provided multiple-choice answers:
- 5,888π cm²
- 1,472π cm²
- 23π cm²
- 368π cm²
To find the original surface area \( SA \) that leads to these options after multiplying by 16:
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For \( 5,888π \):
- \( SA = \frac{5,888π}{16} = 368π \)
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For \( 1,472π \):
- \( SA = \frac{1,472π}{16} = 92π \)
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For \( 23π \):
- \( SA = \frac{23π}{16} = 1.4375π \)
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For \( 368π \):
- \( SA = \frac{368π}{16} = 23π \)
From the calculations, the only option that remains consistent with the multiplication of a specific original surface area by 16 is:
- If the original surface area was \( 368π \), then the new surface area after dilation would be \( 5,888π \).
Since the question asks for the new surface area after dilation and gives us the provided potential answers, the correct answer is:
5,888π cm²