Question

substitute the given values into the given formula and solve for the unknown variable. if necessary, round to one decimal place. $v = \frac{1}{3}pi r^{2}h$, $v = 267.9$, $pi=3.14$, $r = 4$ (volume of a cone). $h=square$ (do not round until the final answer. then round to the nearest tenth as needed.)

Explanation:

Step1: Rearrange volume formula for h

Given $V = \frac{1}{3}\pi r^{2}h$, we can solve for $h$ by multiplying both sides by $3$ and then dividing by $\pi r^{2}$. So $h=\frac{3V}{\pi r^{2}}$.

Step2: Substitute given values

Substitute $V = 267.9$, $\pi=3.14$, and $r = 4$ into the formula for $h$. We get $h=\frac{3\times267.9}{3.14\times4^{2}}$.
First, calculate the denominator: $3.14\times4^{2}=3.14\times16 = 50.24$.
Then, calculate the numerator: $3\times267.9 = 803.7$.
Now, $h=\frac{803.7}{50.24}\approx16.0$.

Answer:

$16.0$