1. **State the problem:** We need to find the approximate radius $r$ of a sphere given its volume $V = 38808$ cubic inches. 2. **Formula:** The radius $r$ is approximated by the formula $$r = \sqrt[3]{\frac{21V}{88}}$$ where $V$ is the volume. 3. **Substitute the given volume:** $$r = \sqrt[3]{\frac{21 \times 38808}{88}}$$ 4. **Calculate the numerator:** $$21 \times 38808 = 814,968$$ 5. **Divide by 88:** $$\frac{814,968}{88} = 9,261$$ 6. **Find the cube root:** $$r = \sqrt[3]{9,261}$$ 7. **Approximate the cube root:** Since $20^3 = 8,000$ and $21^3 = 9,261$, we have $$r \approx 21$$ **Final answer:** The approximate radius of the sphere is $21$ inches.