1. The problem is to explain the mensuration formulas for a cylinder and a sphere. 2. For a cylinder, the important measurements are its radius $r$ and height $h$. 3. The surface area $A$ of a cylinder is given by the formula: $$A = 2\pi r^2 + 2\pi r h$$ This includes the areas of the two circular bases ($2\pi r^2$) and the curved surface area ($2\pi r h$). 4. The volume $V$ of a cylinder is: $$V = \pi r^2 h$$ This represents the space inside the cylinder. 5. For a sphere, the only measurement needed is its radius $r$. 6. The surface area $A$ of a sphere is: $$A = 4\pi r^2$$ This is the total area covering the sphere. 7. The volume $V$ of a sphere is: $$V = \frac{4}{3} \pi r^3$$ This is the space enclosed by the sphere. 8. These formulas are fundamental in geometry and help calculate areas and volumes of these 3D shapes. 9. Remember $\pi$ is approximately 3.1416 and is a constant used in all circle-related calculations.