find the volume of a right circular cone that has a height of 5.1 ft and a base with a diameter of 15.4 ft…

Explanation:

Step1: Calculate base radius

The diameter is 15.4 ft, so radius $r = \frac{15.4}{2} = 7.7$ ft

Step2: Recall cone volume formula

Volume formula: $V = \frac{1}{3}\pi r^2 h$

Step3: Substitute values into formula

Substitute $r=7.7$, $h=5.1$: $$V = \frac{1}{3} \times \pi \times (7.7)^2 \times 5.1$$ First calculate $(7.7)^2 = 59.29$, then $59.29 \times 5.1 = 302.379$ $$V = \frac{1}{3} \times \pi \times 302.379 \approx \frac{949.9}{3}$$

Step4: Compute and round result

$V \approx 316.633$, round to nearest tenth: $316.6$

Answer:

316.6 cubic feet