1. **Problem Statement:** Find the surface area of a semicylindrical solid with radius $r=5$ cm and length $l=8$ cm. 2. **Understanding the shape:** The solid is a half-cylinder (semicylinder) with a semicircular face of radius 5 cm and length 8 cm extending perpendicular to the semicircle. 3. **Formula for surface area of a semicylinder:** The total surface area $A$ consists of: - The curved surface area of the semicylinder - The two flat rectangular faces (top and bottom) - The semicircular face at the front and the flat rectangular face at the back (the base) The curved surface area of a full cylinder is $2\pi r l$, so for a semicylinder it is half: $$\text{Curved surface area} = \pi r l$$ The two flat rectangular faces are each $r \times l$ (since the semicircle height is $r$): $$\text{Two rectangular faces area} = 2rl$$ The base is a rectangle formed by the diameter of the semicircle and the length: $$\text{Base area} = 2r \times l = 2rl$$ The semicircular face area is half the area of a circle: $$\text{Semicircular face area} = \frac{1}{2} \pi r^2$$ 4. **Calculate each part:** - Curved surface area: $\pi \times 5 \times 8 = 40\pi$ - Two rectangular faces: $2 \times 5 \times 8 = 80$ - Base area: $2 \times 5 \times 8 = 80$ - Semicircular face area: $\frac{1}{2} \pi \times 5^2 = \frac{25\pi}{2} = 12.5\pi$ 5. **Sum all areas:** $$A = 40\pi + 80 + 80 + 12.5\pi = (40\pi + 12.5\pi) + 160 = 52.5\pi + 160$$ 6. **Approximate numerical value:** Using $\pi \approx 3.1416$: $$A \approx 52.5 \times 3.1416 + 160 = 164.93 + 160 = 324.93 \text{ cm}^2$$ **Final answer:** The surface area of the semicylindrical solid is approximately $324.93$ cm$^2$.