Density from Area and Volume
Aligned to G-MG.A.2 — Common Core State Standards for Mathematics.
What this lesson teaches
Density is an amount per unit of area or volume. Population density is people per square mile; mass density is mass per unit volume. Compute it by dividing the total quantity by the area or volume it occupies.
Worked example
A metal block has mass 480 grams and volume 60 cubic centimeters. Find its density. Density = mass/volume = 480/60 = 8 grams per cubic centimeter. This lets you compare it to known materials: 8 g/cm^3 is close to the density of iron, so the block is likely an iron alloy.
Practice questions
- A city has 90,000 people in 30 square miles. Find its population density.
- A liquid has mass 250 g and volume 200 cm^3. Find its density in g/cm^3.
- A rectangular field 40 m by 25 m holds 200 trees. Find the tree density per square meter.
Watch the lesson
Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
▶ Watch this lessonEn español
Densidad a partir de área y volumen
La densidad es una cantidad por unidad de área o de volumen. La densidad de población es personas por milla cuadrada; la densidad de masa es masa por unidad de volumen. Se calcula dividiendo la cantidad total entre el área o el volumen que ocupa.
Ejemplo: Un bloque de metal tiene masa 480 gramos y volumen 60 centímetros cúbicos. Halla su densidad. Densidad = masa/volumen = 480/60 = 8 gramos por centímetro cúbico. Esto permite compararlo con materiales conocidos: 8 g/cm^3 se acerca a la densidad del hierro, así que el bloque probablemente es una aleación de hierro.
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