Volume by Displacement — Archimedes' Principle

An irregular solid has volume, but no formula gives it. Archimedes saw that displaced water reveals it. The cylinder is the control. Indirect aim: density, the scientific method, preparation for physics.

• Framework: Montessori
• Unit: Sensorial
• Learning area: Visual Form
• Level: Ages 9-11

Objectives

• Measure volume of an irregular object by water displacement
• Record in milliliters and cubic centimeters
• Understand 1 mL = 1 cm³
• Apply Archimedes' principle

Materials

• Graduated cylinder
• Water
• Various irregular objects (stone, toy, metal nut)
• Recording paper
• Story of Archimedes

Instructions

1. Tell the Archimedes story — the crown, the bath, 'Eureka!'. 2. Fill cylinder with water; read volume V1. 3. Drop object in; read new volume V2. 4. Displacement = V2 - V1 = object's volume. 5. Convert mL to cm³ (same). 6. Repeat with three objects. 7. Compute density if mass is known. 8. Discuss why ships float (buoyancy).

Educator tip

Archimedes ran through Syracuse naked shouting 'Eureka!' — children love this story. It humanizes mathematics.

Assessment

Observe accurate reading, volume calculation, and application to density.

More from Sensorial

• Line Symmetry and Reflection
• Tessellation Study — Regular and Semi-Regular
• Sound Cylinders — Matching Pitches Graded
• Multiplication Chart 1 — The Filled Table
• Multiplication Chart 3 — Bead-Bar Fact Practice
• Prime and Composite — Sieve of Eratosthenes
• Fibonacci Sequence — Patterns in Nature
• Mineral Classification — Mohs Scale