1. **State the problem:** Find the total surface area and volume of a cylinder with height $h=41$ m and radius $r=15$ m. 2. **Formulas:** - Total surface area of a cylinder: $$SA = 2\pi r^2 + 2\pi rh$$ - Volume of a cylinder: $$V = \pi r^2 h$$ 3. **Calculate surface area:** - Calculate the area of the two circular bases: $$2\pi r^2 = 2\pi (15)^2 = 2\pi (225) = 450\pi$$ - Calculate the lateral surface area: $$2\pi rh = 2\pi (15)(41) = 1230\pi$$ - Total surface area: $$SA = 450\pi + 1230\pi = 1680\pi$$ - Approximate using $\pi \approx 3.1416$: $$SA \approx 1680 \times 3.1416 = 5277.88$$ - Rounded to the nearest hundred: $$SA \approx 5300$$ 4. **Calculate volume:** - Volume formula: $$V = \pi r^2 h = \pi (15)^2 (41) = \pi (225)(41) = 9225\pi$$ - Approximate: $$V \approx 9225 \times 3.1416 = 28972.56$$ - Rounded to the nearest hundred: $$V \approx 29000$$ **Final answers:** - Total surface area $\approx 5300$ square meters - Volume $\approx 29000$ cubic meters