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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?

 Feb 25, 2021
 #1
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surface area of cylinder = \(2 \pi rh + 2\pi r^2 = 2\pi r(2.5r) + 2\pi r^2\)

 

\(2\pi r (2.5r) + 2\pi r^2 = 112\pi\)

 

\(2r(2.5r) + 2r^2 = 112\)

 

\(7r^2 = 112\)

 

\(r = \sqrt{\frac{112}{7}} = 4 \quad \rightarrow \quad \boxed{h = 10}\)

 Feb 25, 2021

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