Question

what is the volume of the cone below? a. 852π units³ b. 3408π units³ c. 10,224π units³ d. 5112π units³

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 and $h$ is the height.

Step2: Substitute given values

Here, $r=12$ and $h=71$. Substitute into the formula:
$V = \frac{1}{3}\pi (12)^2 (71)$

Step3: Calculate $r^2$ first

Compute $12^2 = 144$, so:
$V = \frac{1}{3}\pi (144)(71)$

Step4: Simplify $\frac{1}{3} \times 144$

$\frac{1}{3} \times 144 = 48$, so:
$V = 48 \times 71 \times \pi$

Step5: Calculate $48 \times 71$

$48 \times 71 = 3408$, so:
$V = 3408\pi$

Answer:

B. $3408\pi$ units$^3$