The height of a right cylinder is 2.5 times its radius. If the surface area of the cylinder is $112\pi\text{ cm}^2$, what is the radius of the cylinder in centimeters?
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<|im_start|>user
The height of a right cylinder is 2.5 times its radius. If the surface area of the cylinder is $112\pi\text{ cm}^2$, what is the radius of the cylinder in centimeters?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
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The height of a right cylinder is 2.5 times its radius. If the surface area of the cylinder is $112\pi\text{ cm}^2$, what is the radius of the cylinder in centimeters?
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