Question

the volume of this cone is 291.06858 cubic inches. what is the height of this cone? use π ≈ 3.14 and round your answer to the nearest hundredth. h ≈ inches

Explanation:

Step1: Recall volume formula for cone

The volume formula of a cone is $V=\frac{1}{3}\pi r^{2}h$, where $V$ is volume, $r$ is radius and $h$ is height. We know $V = 291.06858$ cubic - inches and $r = 5.3$ inches, $\pi\approx3.14$. We need to solve for $h$.

Step2: Rearrange formula for $h$

Starting from $V=\frac{1}{3}\pi r^{2}h$, we can isolate $h$ by first multiplying both sides by $3$ to get $3V=\pi r^{2}h$. Then divide both sides by $\pi r^{2}$, so $h=\frac{3V}{\pi r^{2}}$.

Step3: Substitute values

Substitute $V = 291.06858$, $\pi\approx3.14$ and $r = 5.3$ into the formula for $h$.
$h=\frac{3\times291.06858}{3.14\times(5.3)^{2}}$
First, calculate $(5.3)^{2}=28.09$. Then $3.14\times28.09 = 88.0026$. And $3\times291.06858 = 873.20574$.
So $h=\frac{873.20574}{88.0026}\approx9.92$.

Answer:

$9.92$