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Measuring Volume by Counting

  • Grade 5
  • Mathematics
  • 5.MD.C.4
  • Measurement & Data
  • Free lesson

Aligned to 5.MD.C.4 — Common Core State Standards for Mathematics.

What this lesson teaches

You can measure the volume of a solid by counting how many unit cubes fill it. We name the units by the cube size, like cubic centimeters (cubic cm) or cubic inches. Count each layer, then add up all the layers.

Worked examples

Example 1

A box is 4 cm wide, 3 cm deep, and 2 cm tall, filled with 1-cm cubes. One layer has 4 × 3 = 12 cubes. There are 2 layers, so 12 + 12 = 24 cubes. The volume is 24 cubic cm.

Example 2

A box 6 cm by 2 cm by 5 cm holds 6 × 2 = 12 cubes per layer, and 5 layers: 12 × 5 = 60 cubic cm.

Example 3

A solid shaped like two boxes stuck together is measured by splitting it: find each box's volume and add them.

Practice questions

  1. A box holds one layer of 5 × 2 unit cubes. How many cubes is that?
  2. A box is 3 units wide, 3 units deep, and 3 units tall. How many cubes fill it?
  3. A box has 10 cubes in each layer and is 4 layers tall. What is its volume in cubic units?

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 lesson

En español

Medir el volumen contando

Puedes medir el volumen de un sólido contando cuántos cubos unitarios lo llenan. Nombramos las unidades según el tamaño del cubo, como centímetros cúbicos (cm cúbicos) o pulgadas cúbicas. Cuenta cada capa y luego suma todas las capas.

Ejemplo 1: Una caja mide 4 cm de ancho, 3 cm de fondo y 2 cm de alto, llena de cubos de 1 cm. Una capa tiene 4 × 3 = 12 cubos. Hay 2 capas, así que 12 + 12 = 24 cubos. El volumen es 24 cm cúbicos.

Ejemplo 2: Una caja de 6 cm por 2 cm por 5 cm tiene 6 × 2 = 12 cubos por capa, y 5 capas: 12 × 5 = 60 cm cúbicos.

Ejemplo 3: Un sólido con forma de dos cajas pegadas se mide separándolo: halla el volumen de cada caja y súmalos.

More Measurement & Data lessons

Volume of Rectangular Prisms5.MD.C.5Unit Conversion and Line Plots5.MD.A.1Line Plots with Fractions5.MD.B.2What Volume Means5.MD.C.3

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