1. **State the problem:** We need to find the radius $r$ of a solid sphere given its volume $V = 70.34$ cubic inches. 2. **Formula for the volume of a sphere:** $$V = \frac{4}{3} \pi r^3$$ where $\pi \approx 3.14$. 3. **Substitute the known values:** $$70.34 = \frac{4}{3} \times 3.14 \times r^3$$ 4. **Simplify the constant term:** $$\frac{4}{3} \times 3.14 = \frac{4 \times 3.14}{3} = \frac{12.56}{3} = 4.1867$$ 5. **Rewrite the equation:** $$70.34 = 4.1867 \times r^3$$ 6. **Isolate $r^3$ by dividing both sides by 4.1867:** $$r^3 = \frac{70.34}{4.1867}$$ 7. **Show cancellation:** $$r^3 = \frac{\cancel{70.34}}{\cancel{4.1867}} = 16.8$$ 8. **Find the cube root of both sides to solve for $r$:** $$r = \sqrt[3]{16.8}$$ 9. **Calculate the cube root:** $$r \approx 2.57$$ 10. **Round to the nearest tenth:** $$r \approx 2.6$$ **Final answer:** The radius of the sphere is approximately **2.6 inches**. This corresponds to choice **A**.