1. **State the problem:** Calculate the surface area (excluding the top rectangle) and volume of a half cylinder with radius $r=34$ cm and length $l=0.58$ m. Convert all units to cm. 2. **Convert length to cm:** $$l = 0.58 \text{ m} = 0.58 \times 100 = 58 \text{ cm}$$ 3. **Calculate the curved surface area of the half cylinder:** The curved surface area of a full cylinder is $2\pi r l$. For a half cylinder, it is half of that: $$\text{Curved surface area} = \pi r l = \pi \times 34 \times 58$$ Calculate: $$\pi \times 34 \times 58 = 3.1416 \times 34 \times 58 = 6193.8 \text{ cm}^2$$ 4. **Calculate the flat rectangular side area:** The flat side is a rectangle with dimensions $l$ by diameter $2r$: $$\text{Flat side area} = l \times 2r = 58 \times (2 \times 34) = 58 \times 68 = 3944 \text{ cm}^2$$ 5. **Calculate total surface area (excluding top rectangle):** The problem states to exclude the top rectangle, so total surface area is curved surface area plus flat side area: $$\text{Surface area} = 6193.8 + 3944 = 10137.8 \text{ cm}^2$$ 6. **Calculate the volume of the half cylinder:** Volume of full cylinder: $$V = \pi r^2 l = \pi \times 34^2 \times 58$$ Calculate: $$\pi \times 1156 \times 58 = 3.1416 \times 1156 \times 58 = 210460.5 \text{ cm}^3$$ Half cylinder volume is half of that: $$\text{Volume} = \frac{210460.5}{2} = 105230.25 \text{ cm}^3$$ **Final answers:** Surface Area = $10137.8$ cm$^2$ Volume = $105230.25$ cm$^3$