Final answer:
Ranking densities requires mass and volume data, which is not provided in the question. Surface areas and volumes for different shapes are discussed, but without mass measurements, density ranking is not possible. Instead, appropriate tools for measuring volume and weight of different items are suggested.
Step-by-step explanation:
To rank the densities of the objects provided, we must first understand that density is calculated as mass per unit volume (ρ = m/V). However, the question does not appear to provide specific mass or volume data for the objects in question. If the objects have equal volumes, as suggested by some of the text, we would need the mass of these objects to calculate and compare their densities.
Without specific mass data, we cannot rank the densities directly. We are provided with information on surface areas and volume relationships for different shapes, but to rank densities, we need either direct measurements or a description of the mass of those shapes. The mention of spheres and cubes with the expression "a³ = 8r³" suggests a relationship between the side length of a cube and the radius of a sphere, but without additional context, we cannot use this to calculate densities.
As for the tools to measure volume and other quantities suggested in the question, here are appropriate tools:
- For the volume of a water balloon, a measuring cup or graduated cylinder could be used.
- To measure the length of a basketball court, a measuring tape or laser distance measurer would be appropriate.
- The weight of an apple can be measured using a kitchen scale.
- And, the volume of a milk carton can be determined from its labeled volume or measured using a graduated cylinder if the carton is not labeled.