1. **State the problem:** We are given the volume of a sphere as $2400$ m³ and asked to find the diameter $d$. 2. **Recall the formula for the volume of a sphere:** $$V = \frac{4}{3} \pi r^3$$ where $r$ is the radius. 3. **Relate diameter and radius:** $$d = 2r$$ 4. **Use the given volume to find $r$:** $$2400 = \frac{4}{3} \pi r^3$$ 5. **Isolate $r^3$:** $$r^3 = \frac{2400 \times 3}{4 \pi} = \frac{7200}{4\pi} = \frac{1800}{\pi}$$ 6. **Calculate $r$ by taking the cube root:** $$r = \sqrt[3]{\frac{1800}{\pi}}$$ 7. **Find the diameter $d$:** $$d = 2r = 2 \times \sqrt[3]{\frac{1800}{\pi}}$$ 8. **Approximate the numerical value:** Using $\pi \approx 3.1416$, $$r \approx \sqrt[3]{\frac{1800}{3.1416}} = \sqrt[3]{573.0} \approx 8.3$$ $$d \approx 2 \times 8.3 = 16.6$$ **Final answer:** $$\boxed{d \approx 16.6 \text{ units}}$$