Question

the volume of this cone is 103.62 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 $V = 103.62$ cubic - inches and $r = 3$ inches and $\pi\approx3.14$.

Step2: Rearrange formula for height

From $V=\frac{1}{3}\pi r^{2}h$, we can solve for $h$. First, multiply both sides by $3$ to get $3V=\pi r^{2}h$. Then, $h=\frac{3V}{\pi r^{2}}$.

Step3: Substitute values

Substitute $V = 103.62$, $\pi\approx3.14$ and $r = 3$ into the formula for $h$. So $h=\frac{3\times103.62}{3.14\times3^{2}}$.

Step4: Calculate the value of h

First, calculate the denominator: $3.14\times3^{2}=3.14\times9 = 28.26$. Then, calculate the numerator: $3\times103.62 = 310.86$. Now, $h=\frac{310.86}{28.26}=11.00$.

Answer:

$11.00$