1. **Problem Statement:** Find the surface area of a cylinder and a cone. 2. **Formulas:** - Surface area of a cylinder: $$A_{cyl} = 2\pi r h + 2\pi r^2$$ where $r$ is the radius and $h$ is the height. - Surface area of a cone: $$A_{cone} = \pi r l + \pi r^2$$ where $r$ is the radius and $l$ is the slant height. 3. **Explanation:** - For the cylinder, the surface area consists of the lateral area $2\pi r h$ plus the area of the two circular bases $2\pi r^2$. - For the cone, the surface area consists of the lateral area $\pi r l$ plus the base area $\pi r^2$. 4. **Example Calculation:** - Suppose a cylinder has radius $r=3$ and height $h=5$. - Calculate lateral area: $$2\pi \times 3 \times 5 = 30\pi$$ - Calculate base area: $$2\pi \times 3^2 = 18\pi$$ - Total surface area cylinder: $$30\pi + 18\pi = 48\pi$$ - Suppose a cone has radius $r=3$ and slant height $l=5$. - Calculate lateral area: $$\pi \times 3 \times 5 = 15\pi$$ - Calculate base area: $$\pi \times 3^2 = 9\pi$$ - Total surface area cone: $$15\pi + 9\pi = 24\pi$$ 5. **Summary:** - Cylinder surface area: $$48\pi$$ - Cone surface area: $$24\pi$$ These formulas and steps help you find the surface areas of cylinders and cones easily.