what is the volume of a hemisphere with a diameter of 4.6 ft, rounded to the nearest tenth of a cubic foot?

Explanation:

Step1: Find radius from diameter

The radius $r$ is half the diameter: $r = \frac{4.6}{2} = 2.3$ ft

Step2: Recall hemisphere volume formula

The volume $V$ of a hemisphere is half the volume of a sphere: $V = \frac{2}{3}\pi r^3$

Step3: Substitute radius into formula

$V = \frac{2}{3} \times \pi \times (2.3)^3$ First calculate $(2.3)^3 = 2.3 \times 2.3 \times 2.3 = 12.167$ Then: $V = \frac{2}{3} \times \pi \times 12.167 \approx \frac{2}{3} \times 38.22 \approx 25.48$

Step4: Round to nearest tenth

Round 25.48 to one decimal place: $25.5$

Answer:

25.5 cubic feet