Question

substitute the given values into the given formula and solve for the unknown variable. if necessary, round to one decimal place. v = 1/3πr²h; v = 666.7, π = 3.14, r = 7 (volume of a cone) h = □ (do not round until the final answer. then round to the nearest tenth as needed.)

Explanation:

Step1: Substitute given values into formula

Given $V = 666.7$, $\pi=3.14$, $r = 7$ and the volume formula of a cone $V=\frac{1}{3}\pi r^{2}h$. Substitute these values: $666.7=\frac{1}{3}\times3.14\times7^{2}\times h$.

Step2: Simplify the right - hand side

First, calculate $7^{2}=49$, then $\frac{1}{3}\times3.14\times49\times h=\frac{3.14\times49}{3}h=\frac{153.86}{3}h$. So the equation becomes $666.7=\frac{153.86}{3}h$.

Step3: Solve for h

Multiply both sides of the equation by $\frac{3}{153.86}$ to isolate $h$. $h = 666.7\times\frac{3}{153.86}$.
$h=\frac{2000.1}{153.86}\approx13.0$.

Answer:

$13.0$