Learn on PengiIllustrative Mathematics, Grade 8Chapter 8: Pythagorean Theorem and Irrational Numbers

Lesson 3: Side Lengths and Volumes of Cubes

In this Grade 8 Illustrative Mathematics lesson from Chapter 8: Pythagorean Theorem and Irrational Numbers, students explore the relationship between the side lengths and volumes of cubes, building understanding of how to find an unknown side length when the volume is known. The lesson lays the groundwork for cube roots and irrational numbers by asking students to reason about perfect and non-perfect cube volumes. This connects directly to the chapter's broader focus on number types and geometric measurement.

Section 1

Volume of a Cube

Property

A cube is a rectangular prism whose length, width, and height are all equal. For any cube with sides of length ss:

Volume: V=s3V = s^3

Section 2

Application: Finding Edge Length from the Volume of a Cube

Property

The volume VV of a cube with an edge length of ss is given by the formula V=s3V = s^3. To find the edge length of a cube from its volume, you must find the cube root of the volume.

s=V3s = \sqrt[3]{V}

Examples

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Chapter 8: Pythagorean Theorem and Irrational Numbers

  1. Lesson 1

    Lesson 1: Side Lengths and Areas of Squares

  2. Lesson 2

    Lesson 2: The Pythagorean Theorem

  3. Lesson 3Current

    Lesson 3: Side Lengths and Volumes of Cubes

  4. Lesson 4

    Lesson 4: Decimal Representation of Rational and Irrational Numbers

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Volume of a Cube

Property

A cube is a rectangular prism whose length, width, and height are all equal. For any cube with sides of length ss:

Volume: V=s3V = s^3

Section 2

Application: Finding Edge Length from the Volume of a Cube

Property

The volume VV of a cube with an edge length of ss is given by the formula V=s3V = s^3. To find the edge length of a cube from its volume, you must find the cube root of the volume.

s=V3s = \sqrt[3]{V}

Examples

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 8: Pythagorean Theorem and Irrational Numbers

  1. Lesson 1

    Lesson 1: Side Lengths and Areas of Squares

  2. Lesson 2

    Lesson 2: The Pythagorean Theorem

  3. Lesson 3Current

    Lesson 3: Side Lengths and Volumes of Cubes

  4. Lesson 4

    Lesson 4: Decimal Representation of Rational and Irrational Numbers