1. Let's state the problem: We want to understand the properties of a coin modeled as a cylinder. 2. A cylinder is a 3D shape with two parallel circular bases connected by a curved surface. 3. The main formulas for a cylinder are: - Volume: $$V = \pi r^2 h$$ where $r$ is the radius of the base and $h$ is the height (thickness) of the cylinder. - Surface Area: $$A = 2\pi r^2 + 2\pi r h$$ which includes the areas of the two circular bases and the curved surface. 4. Important rules: - The radius $r$ is half the diameter of the coin. - The height $h$ is the thickness of the coin. 5. To find the volume or surface area of the coin, measure the radius and thickness, then substitute into the formulas. 6. Example: If a coin has a radius of 1.2 cm and thickness of 0.2 cm, - Volume: $$V = \pi (1.2)^2 (0.2) = \pi \times 1.44 \times 0.2 = 0.288\pi \approx 0.904\text{ cm}^3$$ - Surface Area: $$A = 2\pi (1.2)^2 + 2\pi (1.2)(0.2) = 2\pi (1.44) + 2\pi (0.24) = 2.88\pi + 0.48\pi = 3.36\pi \approx 10.55\text{ cm}^2$$ This approach helps understand the physical properties of a coin modeled as a cylinder.