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The feathers in a pillow have a total mass of 59 grams. The pillow is in the shape of a rectangular prism measuring 51 cm by 66 cm by 7 cm.
A steel anchor is shaped like a square pyramid. Each side of the base measures 20 cm, and its height is 28 cm. The anchor’s mass is 30 kg.
Students may calculate density in grams per cm3, then be unsure how to convert to kg per m3. Prompt them to either convert the measurements to cubic meters and kilograms prior to calculating density, or to use dimensional analysis to convert the density.
The purpose of this discussion is to draw out relationships between mass, volume, and density. Ask students:
An aquarium manager drew a blueprint for a cylindrical fish tank. The tank has a vertical tube in the middle in which visitors can stand and view the fish.
The best average density for the species of fish that will go in the tank is 16 fish per 100 gallons of water. This provides enough room for the fish to swim while making sure that there are plenty of fish for people to see. There are 7.48 gallons of water in 1 cubic foot.
The aquarium has 275 fish available to put in the tank. Is this the right number of fish for the tank? If not, how many fish should be added or removed? Explain your reasoning.
The goal of this discussion is to highlight different ways to solve the problem. Ask students what the density of fish per 100 gallons would be if 275 fish were put in the tank, and what that means in this situation. Invite students to share how they approached rounding. For example, if the calculations show that 315.8 fish are needed, should we round up or down? Both answers can be supported.