1. **State the problem:** Find the lateral surface area and volume of a right circular cylinder with radius $r=41.4$ cm and height $h=80.9$ cm. 2. **Formulas:** - Lateral surface area $A = 2\pi r h$ - Volume $V = \pi r^2 h$ 3. **Calculate lateral surface area:** $$A = 2\pi (41.4)(80.9)$$ $$A = 2\pi \times 3350.26$$ $$A = 2 \times 3.1416 \times 3350.26$$ $$A = 21052.36\text{ cm}^2$$ 4. **Calculate volume:** $$V = \pi (41.4)^2 (80.9)$$ $$V = \pi \times 1713.96 \times 80.9$$ $$V = 3.1416 \times 138592.76$$ $$V = 435388.15\text{ cm}^3$$ 5. **Final answers rounded to nearest hundredth:** - Lateral surface area $= 21052.36\text{ cm}^2$ - Volume $= 435388.15\text{ cm}^3$