Question

find the volume of a right circular cone that has a height of 17.4 m and a base with a diameter of 3.1 m. round your answer to the nearest tenth of a cubic meter.

Explanation:

Step1: Calculate base radius

The radius $r$ is half the diameter.
$r = \frac{3.1}{2} = 1.55$ m

Step2: Recall cone volume formula

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

Step3: Substitute values into formula

Plug $r=1.55$ m and $h=17.4$ m into the formula.
$V = \frac{1}{3} \times \pi \times (1.55)^2 \times 17.4$
First calculate $(1.55)^2 = 2.4025$, then multiply by 17.4: $2.4025 \times 17.4 = 41.8035$.
Then multiply by $\frac{1}{3}\pi$: $V = \frac{41.8035}{3} \times \pi \approx 13.9345 \times 3.1416 \approx 43.8$

Answer:

$43.8$ cubic meters