Question

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 = 489.8, \\(\pi\\) = 3.14, r = 6 (volume of a cone) h = \\(\square\\) (do not round until the final answer. then round to the nearest tenth as needed.)

Explanation:

Step1: Substitute given values into formula

Given $V = \frac{1}{3}\pi r^{2}h$, substitute $V = 489.8$, $\pi=3.14$, and $r = 6$.
So, $489.8=\frac{1}{3}\times3.14\times6^{2}\times h$.

Step2: Simplify the right - hand side

First, calculate $6^{2}=36$. Then $\frac{1}{3}\times3.14\times36\times h=( \frac{1}{3}\times36)\times3.14\times h = 12\times3.14\times h=37.68h$.
The equation becomes $489.8 = 37.68h$.

Step3: Solve for h

Divide both sides of the equation by 37.68: $h=\frac{489.8}{37.68}$.
$h\approx13.0$.

Answer:

$13.0$