1. **State the problem:** We have a solid cylinder of height 11 m and radius 4 m. A cone is removed from the top of the cylinder. The cone has the same base radius 4 m and a slant height of 9 m. We need to find the total surface area of the resulting shape in terms of $\pi$. 2. **Identify the surfaces involved:** - The cylinder has two circular bases and a curved surface. - The cone removed removes the top circular base of the cylinder and creates a slant surface inside. 3. **Surface area of the original cylinder:** - Curved surface area of cylinder = $2\pi rh = 2\pi \times 4 \times 11 = 88\pi$ - Area of one base = $\pi r^2 = \pi \times 4^2 = 16\pi$ - Total surface area of cylinder = curved surface + 2 bases = $88\pi + 2 \times 16\pi = 88\pi + 32\pi = 120\pi$ 4. **Effect of removing the cone:** - The top base of the cylinder is removed, so we lose $16\pi$. - The cone's slant surface is exposed inside the shape. 5. **Calculate the lateral surface area of the cone:** - Lateral surface area of cone = $\pi r l = \pi \times 4 \times 9 = 36\pi$ 6. **Total surface area of the shape:** - Bottom base of cylinder remains: $16\pi$ - Curved surface of cylinder remains: $88\pi$ - Cone's slant surface exposed: $36\pi$ Add these: $$16\pi + 88\pi + 36\pi = 140\pi$$ **Final answer:** The total surface area of the shape is $\boxed{140\pi}$ square meters.