Question

the volume of this cone is 241.152 cubic inches. what is the radius of this cone? round your answer to the nearest hundredth. 6.4 in r ≈ \boxed{} inches submit

Explanation:

Step1: Recall cone volume formula

The volume $V$ of a cone is $V = \frac{1}{3}\pi r^2 h$, where $r$ is radius, $h=6.4$ in, $V=241.152$ cubic inches.

Step2: Rearrange to solve for $r^2$

Multiply both sides by 3, divide by $\pi h$:
$r^2 = \frac{3V}{\pi h}$

Step3: Substitute known values

$r^2 = \frac{3\times241.152}{\pi\times6.4}$
Calculate numerator: $3\times241.152=723.456$
Calculate denominator: $\pi\times6.4\approx20.1062$
$r^2 \approx \frac{723.456}{20.1062}\approx36.0$

Step4: Solve for $r$

Take square root: $r = \sqrt{36.0}=6.00$

Answer:

$6.00$ inches