Question

the volume of this cone is 8,242.5 cubic millimeters. what is the height of this cone? round your answer to the nearest hundredth. 15 mm h ≈ millimeters

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 $V = 8242.5$ mm³ and $r = 15$ mm.

Step2: Rearrange formula for height

From $V=\frac{1}{3}\pi r^{2}h$, we can solve for $h$: $h=\frac{3V}{\pi r^{2}}$.

Step3: Substitute values

Substitute $V = 8242.5$, $r = 15$ and $\pi\approx3.14$ into the formula: $h=\frac{3\times8242.5}{3.14\times15^{2}}$.
First, calculate $15^{2}=225$, then $3.14\times225 = 706.5$, and $3\times8242.5=24727.5$.
So $h=\frac{24727.5}{706.5}$.

Step4: Calculate the value of h

$h=\frac{24727.5}{706.5}=35.00$

Answer:

$35.00$