Shape and Density

This worksheet develops understanding of density as an intrinsic property that does not change when an object is cut, reshaped, or scaled uniformly. Students solve problems about equal-sized pieces, compressed volumes, and spheres of different radii to reason how mass and volume scale together. They predict floating or sinking by comparing object density to water and explain cases where objects made of dense materials (e.g., steel boats) still float due to overall volume and displacement. Items ask learners to interpret percent of volume above water, relate it to density ratios, and justify answers mathematically. Additional prompts contrast objects with the same material but different shapes, reinforcing that shape affects buoyancy through displaced volume, not density itself. Throughout, students practice quantitative reasoning, geometric scaling, and clear scientific explanation.

Curriculum Matched Skills

Physical Science – Intrinsic Properties of Matter (density invariance)

Science – Buoyancy and Fluid Mechanics (Archimedes’ principle concepts)

Mathematics – Geometry of Scaling and Proportional Relationships

Science – Quantitative Problem Solving and Justification

This worksheet is part of our Density collection.