Volume City Builder Lab

Design buildings by stacking unit cubes. Calculate their volumes, compare different shapes, and complete city-building missions.

Guided Experiment: Volume City Builder Investigation

If you change only the height of a building but keep length and width the same, what happens to the volume? Make a prediction.

Write your hypothesis in the Lab Report panel, then click Next.

Choose Your Mission

Build all 3 buildings with a volume of 24 cubic units each. Can you make them all look different?

Controls

Length
2
Width
2
Height
3
Volume
12
cubic units
Length
3
Width
2
Height
2
Volume
12
cubic units
Length
1
Width
4
Height
3
Volume
12
cubic units

City Skyline

Total city volume:36 cubic units
12 cubes
2x2x3
Building 1
12 cubes
3x2x2
Building 2
12 cubes
1x4x3
Building 3
Keep going -- each building needs a volume of 24 cubic units.

Data Table

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#BuildingLengthWidthHeightVolume (cubic units)
0 / 500
0 / 500
0 / 500

Reference Guide

Volume Formula

Volume tells us how much space a 3D shape takes up. For a rectangular prism:

Volume = Length x Width x Height

Volume is measured in cubic units (cm3, in3, unit3).

Same Volume, Different Shape

Many different shapes can have the same volume. A 1x2x12 box has the same volume as a 2x3x4 box -- both equal 24 cubic units.

This is why architects have many choices when designing buildings!

Layers of Cubes

Think of volume as layers. Each layer has Length x Width cubes. Stack Height layers to get the total volume.

Example: A 3x4 base with 2 layers high = 3 x 4 x 2 = 24 cubes.

City Planning

Real city planners use volume to calculate how much space is in a building and how many people it can hold.

Skyscrapers are tall and thin. Warehouses are wide and flat. Both can have the same volume!