1. Let's clarify the problem: We are dealing with a frustum of a cone, where $R$ is the radius of the larger base, $r$ is the radius of the smaller base, and the slant height $l$ is the length of the side between the two bases. 2. The formula for the slant height $l$ of a frustum is derived from the right triangle formed by the height $h$, and the difference in radii $R-r$ as the base of the triangle: $$l = \sqrt{h^2 + (R-r)^2}$$ 3. Important rule: The slant height is the hypotenuse of a right triangle where one leg is the vertical height $h$ and the other leg is the difference in radii $R-r$, not just $R$. 4. Why subtract $r$ from $R$? Because the slant height measures the distance along the side between the two circular edges, so the horizontal leg of the triangle is the difference between the two radii, not the full radius $R$. 5. Using only $R$ would imply the smaller base radius is zero, which is not the case in a frustum. 6. Therefore, the correct expression for the slant height is: $$l = \sqrt{h^2 + (R-r)^2}$$ This ensures the slant height correctly accounts for the tapering of the frustum from radius $R$ to radius $r$.