Answer:
[tex]\boxed{\text{14 in}^{2}}[/tex]
Step-by-step explanation:
The scale factor (C) is the ratio of corresponding parts of the two cylinders.
The ratio of the areas is the square of the scale factor.
[tex]\dfrac{A_{1}}{ A_{2}} = C^{2}\\ \\\dfrac{224}{ A_{2}} = \left (\dfrac{1}{\frac{1}{4}} \right )^{2}\\\\\dfrac{224}{ A_{2}}= 16\\A_{2} = \dfrac{224}{16\\\\}[/tex]
A₂ = 14 in²
The surface area of the new cylinder will be [tex]\boxed{\textbf{14 in}^{2}}[/tex].
