Question: curved surface area of a cone = $\pi rl$ where $r$ is the radius and $l$ is the slant height. A shape is formed by removing a cone from the top of a solid cylinder, as shown below. Calculate the total surface area of the shape in terms of $\pi$. Graph/shape: bottom-right, a solid cylinder with a cone-shaped cavity removed from the top; the cone slant height is $9$ m, the cylinder height is $11$ m, and the base radius is $4$ m.

1. **State the problem:** We have a solid cylinder of height $11$ m and radius $4$ m. A cone with the same base radius $4$ m and slant height $9$ m is removed from the top of the cylinder. We need to find the total surface area of the resulting shape in terms of $\pi$. 2. **Identify the surfaces involved:** - The bottom base of the cylinder (circle of radius $4$ m). - The curved surface area of the cylinder (excluding the top base since it is removed). - The curved surface area of the cone cavity (the inside surface of the removed cone). 3. **Formulas:** - Curved surface area of a cylinder: $$2\pi rh$$ where $r$ is radius and $h$ is height. - Area of a circle (base): $$\pi r^2$$. - Curved surface area of a cone: $$\pi rl$$ where $r$ is radius and $l$ is slant height. 4. **Calculate each part:** - Bottom base area of cylinder: $$\pi \times 4^2 = 16\pi$$. - Curved surface area of cylinder: $$2\pi \times 4 \times 11 = 88\pi$$. - Curved surface area of cone cavity: $$\pi \times 4 \times 9 = 36\pi$$. 5. **Total surface area of the shape:** Since the top base of the cylinder is removed and replaced by the cone cavity, the top surface is the curved surface of the cone cavity. So total surface area = bottom base area + curved surface area of cylinder + curved surface area of cone cavity $$= 16\pi + 88\pi + 36\pi = 140\pi$$. **Final answer:** $$\boxed{140\pi}$$