Substitute the given values into the given formula and solve for the unknown variable. If necessary, round to one decimal place. \[ V=\frac{1}{3} \pi r^{2} h ; V=418.7, \pi=3.14, r=5 \text { (volume of a cone) } \]

To find the height \( h \) of the cone, we start by substituting the known values into the formula: \[ 418.7 = \frac{1}{3} \times 3.14 \times 5^2 \times h \] Calculating this step by step, we first evaluate \( 5^2 \), which is \( 25 \): \[ 418.7 = \frac{1}{3} \times 3.14 \times 25 \times h \] Next, find \( \frac{1}{3} \times 3.14 \times 25 \): \[ \frac{1}{3} \times 3.14 = 1.047 \] and then \( 1.047 \times 25 = 26.175 \). Replacing this back into the equation gives us: \[ 418.7 = 26.175 \times h \] Now, to solve for \( h \), divide both sides by \( 26.175 \): \[ h = \frac{418.7}{26.175} \] Calculating this: \[ h \approx 15.97 \] Rounding to one decimal place, the height \( h \) is approximately \( 16.0 \).