1. **State the problem:** Find the volume of a cone using the formula $$V = \frac{1}{3} \pi r^2 h$$ where $r$ is the radius and $h$ is the height. 2. **Formula and rules:** The volume of a cone is one-third the product of the base area ($\pi r^2$) and the height $h$. 3. **Calculate volume for the first cone:** Given $r=4$ m and $h=10$ m, $$V = \frac{1}{3} \times 3.14 \times 4^2 \times 10$$ $$= \frac{1}{3} \times 3.14 \times 16 \times 10$$ $$= \frac{1}{3} \times 3.14 \times 160$$ $$= \frac{1}{3} \times 502.4$$ $$= \cancel{\frac{1}{3}} \times 502.4$$ $$= 167.466\ldots$$ Rounded to the nearest tenth, the volume is $167.5$ cubic meters. 4. **Calculate volume for the second cone:** Given $r=2$ cm and $h=7$ cm, $$V = \frac{1}{3} \times 3.14 \times 2^2 \times 7$$ $$= \frac{1}{3} \times 3.14 \times 4 \times 7$$ $$= \frac{1}{3} \times 3.14 \times 28$$ $$= \frac{1}{3} \times 87.92$$ $$= 29.306\ldots$$ Rounded to the nearest tenth, the volume is $29.3$ cubic centimeters. 5. **Calculate volume for the third cone:** Given $r=5$ mm and $h=15$ mm, $$V = \frac{1}{3} \times 3.14 \times 5^2 \times 15$$ $$= \frac{1}{3} \times 3.14 \times 25 \times 15$$ $$= \frac{1}{3} \times 3.14 \times 375$$ $$= \frac{1}{3} \times 1177.5$$ $$= 392.5$$ The volume is exactly $392.5$ cubic millimeters. 6. **Calculate volume for the fourth cone:** Given $r=6$ cm and $h=7$ cm, $$V = \frac{1}{3} \times 3.14 \times 6^2 \times 7$$ $$= \frac{1}{3} \times 3.14 \times 36 \times 7$$ $$= \frac{1}{3} \times 3.14 \times 252$$ $$= \frac{1}{3} \times 791.28$$ $$= 263.76$$ Rounded to the nearest tenth, the volume is $263.8$ cubic centimeters. 7. **Calculate volume for the fifth cone:** Given $r=10$ m and $h=23$ m, $$V = \frac{1}{3} \times 3.14 \times 10^2 \times 23$$ $$= \frac{1}{3} \times 3.14 \times 100 \times 23$$ $$= \frac{1}{3} \times 3.14 \times 2300$$ $$= \frac{1}{3} \times 7222$$ $$= 2407.333\ldots$$ Rounded to the nearest tenth, the volume is $2407.3$ cubic meters. 8. **Calculate volume for the sixth cone:** Given $r=5$ mm and $h=6$ mm, $$V = \frac{1}{3} \times 3.14 \times 5^2 \times 6$$ $$= \frac{1}{3} \times 3.14 \times 25 \times 6$$ $$= \frac{1}{3} \times 3.14 \times 150$$ $$= \frac{1}{3} \times 471$$ $$= 157$$ The volume is exactly $157$ cubic millimeters. **Final answers:** 1. $167.5$ m³ 2. $29.3$ cm³ 3. $392.5$ mm³ 4. $263.8$ cm³ 5. $2407.3$ m³ 6. $157$ mm³