Question

the volume of this cone is 6,443.28 cubic yards. what is the radius of this cone?
round your answer to the nearest hundredth.
19 yd
$r \approx \square$ yards
save answer

Explanation:

Step1: Recall cone volume formula

The volume $V$ of a cone is given by:
$$V = \frac{1}{3}\pi r^2 h$$
where $r$ is the radius, $h=19$ yd is the height, and $V=6443.28$ cubic yards.

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

$$r^2 = \frac{3 \times 6443.28}{\pi \times 19}$$
Calculate numerator: $3 \times 6443.28 = 19329.84$
Calculate denominator: $\pi \times 19 \approx 59.6903$
$$r^2 \approx \frac{19329.84}{59.6903} \approx 323.835$$

Step4: Take square root for $r$

$$r \approx \sqrt{323.835} \approx 17.995$$

Step5: Round to nearest hundredth

$$r \approx 18.00$$

Answer:

$18.00$ yards