1. **State the problem:** We need to find the exact volumes of a cylinder and a cone, both with radius $r=7$ mm and height $h=6$ mm. 2. **Formulas:** - Volume of a cylinder: $$V_{cyl} = \pi r^2 h$$ - Volume of a cone: $$V_{cone} = \frac{1}{3} \pi r^2 h$$ 3. **Calculate the cylinder volume:** $$V_{cyl} = \pi \times 7^2 \times 6 = \pi \times 49 \times 6 = 294\pi$$ 4. **Calculate the cone volume:** $$V_{cone} = \frac{1}{3} \pi \times 7^2 \times 6 = \frac{1}{3} \pi \times 49 \times 6$$ Simplify the multiplication inside: $$= \frac{1}{3} \pi \times 294$$ Cancel common factor 3: $$= \pi \times \cancel{\frac{1}{3}} \times \cancel{294}$$ Actually, write explicitly: $$= \pi \times \frac{294}{3} = 98\pi$$ 5. **Final answers:** - Cylinder volume: $$294\pi\ \text{mm}^3$$ - Cone volume: $$98\pi\ \text{mm}^3$$