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# cylinders

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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

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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