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

Explanation:

Step1: Recall cone volume formula

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

Step2: Isolate $r^2$ term

Rearrange formula to solve for $r^2$:
$r^2 = \frac{3V}{\pi h}$

Step3: Substitute given values

Substitute $V=278.832$, $h=7.4$, $\pi\approx3.1416$:
$r^2 = \frac{3\times278.832}{3.1416\times7.4}$

Step4: Calculate numerator and denominator

Numerator: $3\times278.832=836.496$
Denominator: $3.1416\times7.4\approx23.24784$
$r^2 \approx \frac{836.496}{23.24784}\approx35.981$

Step5: Solve for $r$

Take square root of $r^2$:
$r \approx \sqrt{35.981}\approx5.998$

Step6: Round to nearest hundredth

Round $5.998$ to two decimal places: $r\approx6.00$

Answer:

6.00 inches