1. **State the problem:** Calculate the volume of a cone with radius $r=4$ inches and height $h=10$ inches. 2. **Formula:** The volume $V$ of a cone is given by $$V=\frac{1}{3}\pi r^2 h$$ where $r$ is the radius of the base and $h$ is the height. 3. **Substitute the values:** $$V=\frac{1}{3}\pi (4)^2 (10)$$ 4. **Calculate the square of the radius:** $$4^2=16$$ 5. **Multiply inside the formula:** $$V=\frac{1}{3}\pi \times 16 \times 10$$ 6. **Simplify the multiplication:** $$V=\frac{1}{3}\pi \times 160$$ 7. **Divide 160 by 3:** $$V=\pi \times \cancel{\frac{160}{3}}\approx \pi \times 53.3333$$ 8. **Multiply by $\pi \approx 3.1416$:** $$V \approx 3.1416 \times 53.3333 = 167.5516$$ 9. **Round to the nearest tenth:** $$V \approx 167.6$$ cubic inches. **Final answer:** The volume of the cone is approximately **167.6** cubic inches.