what is the diameter of a sphere with a volume of 38,383 m³, to the nearest tenth of a meter?

Explanation:

Step1: Recall sphere volume formula

The volume $V$ of a sphere is $V = \frac{4}{3}\pi r^3$, where $r$ is radius.

Step2: Substitute given volume

Substitute $V=38383$: $$38383 = \frac{4}{3}\pi r^3$$

Step3: Solve for $r^3$

Rearrange to isolate $r^3$: $$r^3 = \frac{38383 \times 3}{4\pi} = \frac{115149}{4\pi} \approx \frac{115149}{12.5664} \approx 9163.3$$

Step4: Calculate radius $r$

Take cube root of $r^3$: $$r = \sqrt[3]{9163.3} \approx 20.9$$

Step5: Find diameter $d$

Diameter $d=2r$: $$d = 2 \times 20.9 = 41.8$$

Answer:

$41.8$ meters