Question

what is the volume of this cone? round your answer to the nearest hundredth. 4 mm 3 mm cubic millimeters

Explanation:

Step1: Recall volume formula

The volume formula for a cone is $V=\frac{1}{3}\pi r^{2}h$, where $r$ is the radius and $h$ is the height. Here $r = 3$ mm and $h=4$ mm.

Step2: Substitute values

Substitute $r = 3$ and $h = 4$ into the formula: $V=\frac{1}{3}\times\pi\times3^{2}\times4$.
First, calculate $3^{2}=9$. Then the expression becomes $V=\frac{1}{3}\times\pi\times9\times4$.
$\frac{1}{3}\times9 = 3$, so $V=3\times\pi\times4=12\pi$.

Step3: Calculate and round

Using $\pi\approx3.14159$, $V\approx12\times3.14159 = 37.69908$.
Rounding to the nearest hundredth, $V\approx37.70$ $mm^{3}$.

Answer:

$37.70$