Question

what is the volume of a cone with a radius of 3 and a height of 19? a. 39.79 units³ b. 537.21 units³ c. 1083 units³ d. 179.07 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 radius and $h$ is height.

Step2: Substitute given values

Substitute $r=3$, $h=19$, and $\pi\approx3.1416$:
$V = \frac{1}{3} \times 3.1416 \times 3^2 \times 19$

Step3: Calculate step-by-step

First compute $3^2=9$, then:
$V = \frac{1}{3} \times 3.1416 \times 9 \times 19 = 3.1416 \times 3 \times 19 = 3.1416 \times 57$

Step4: Compute final value

$3.1416 \times 57 \approx 179.07$

Answer:

D. 179.07 units$^3$