cylinders

surface area of cylinder = $2 \pi rh + 2\pi r^2 = 2\pi r(2.5r) + 2\pi r^2$

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

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

$7r^2 = 112$

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