Question

the volume of this cone is 278.832 cubic inches. what is the radius of this cone? round your answer to the nearest hundredth. 7.4 in r ≈ inches submit

Explanation:

Step1: Recall cone volume formula

The volume of a cone is $V = \frac{1}{3}\pi r^2 h$, where $V=278.832$, $h=7.4$.

Step2: Isolate $r^2$ term

Rearrange formula: $r^2 = \frac{3V}{\pi h}$
Substitute values: $r^2 = \frac{3 \times 278.832}{\pi \times 7.4}$

Step3: Calculate $r^2$ value

Compute numerator: $3 \times 278.832 = 836.496$
Compute denominator: $\pi \times 7.4 \approx 23.2478$
$r^2 \approx \frac{836.496}{23.2478} \approx 35.98$

Step4: Solve for $r$

Take square root: $r \approx \sqrt{35.98}$

Answer:

$r \approx 5.99$ inches