Final answer:
The lightest open-top right circular cylinder with a volume of 1000 cm³ requires finding the minimal surface area for the given volume. The formulas V = πr²h and A = 2πrh + πr² are used to describe volume and surface area, respectively. Exact dimensions require calculus to determine the minimal surface area while adhering to the volume constraint.
Step-by-step explanation:
The question is seeking the dimensions of the lightest open-top right circular cylinder with a volume of 1000 cm³. To determine the lightest cylinder, we must consider the surface area because the material used for the cylinder correlates with its surface area, affecting its weight. To find the dimensions that yield the minimal surface area for a fixed volume, we can use the formulas for the volume and surface area of a cylinder.
The volume V of a right circular cylinder is given by V = πr²h, where r is the radius and h is the height. Given that V is 1000 cm³, it means the height and radius must satisfy this equation. However, to find the dimensions that make the cylinder the lightest, we must also consider the total surface area without the top (since it's open-top), which is A = 2πrh + πr². Using calculus, we can minimize this surface area under the constraint of the given volume to find the optimal dimensions. Unfortunately, without further calculation or information provided, we cannot specify the exact dimensions.