Learn on PengienVision, Mathematics, Grade 6Chapter 7: Solve Area, Surface Area, and Volume Problems

Lesson 8: Find Volume with Fractional Edge Lengths

In this Grade 6 enVision Mathematics lesson, students learn how to calculate the volume of rectangular prisms with fractional and decimal edge lengths by applying the volume formula V = l × w × h. The lesson covers multiplying mixed numbers and decimals to find volume, as well as working backwards from a known volume to find a missing dimension. These skills are practiced through real-world problems involving objects like gift boxes, school lockers, and shipping boxes.

Section 1

Volume

Property

We use cubic units to measure the volume or amount of space inside a three-dimensional object. For a box with dimensions length ll, width ww, and height hh, the volume is found by multiplying the three dimensions.

V=l×w×hV = l \times w \times h

Examples

  • An aquarium is 3 feet long, 1.5 feet wide, and 2 feet tall. Its volume is 3×1.5×2=93 \times 1.5 \times 2 = 9 cubic feet.
  • A shoebox has dimensions of 14 inches by 8 inches by 5 inches. Its volume is 14×8×5=56014 \times 8 \times 5 = 560 cubic inches.

Section 2

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

Book overview

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Chapter 7: Solve Area, Surface Area, and Volume Problems

  1. Lesson 1

    Lesson 1: Find Areas of Parallelograms and Rhombuses

  2. Lesson 2

    Lesson 2: Solve Triangle Area Problems

  3. Lesson 3

    Lesson 3: Find Areas of Trapezoids and Kites

  4. Lesson 4

    Lesson 4: Find Areas of Polygons

  5. Lesson 5

    Lesson 5: Represent Solid Figures Using Nets

  6. Lesson 6

    Lesson 6: Find Surface Areas of Prisms

  7. Lesson 7

    Lesson 7: Find Surface Areas of Pyramids

  8. Lesson 8Current

    Lesson 8: Find Volume with Fractional Edge Lengths

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Volume

Property

We use cubic units to measure the volume or amount of space inside a three-dimensional object. For a box with dimensions length ll, width ww, and height hh, the volume is found by multiplying the three dimensions.

V=l×w×hV = l \times w \times h

Examples

  • An aquarium is 3 feet long, 1.5 feet wide, and 2 feet tall. Its volume is 3×1.5×2=93 \times 1.5 \times 2 = 9 cubic feet.
  • A shoebox has dimensions of 14 inches by 8 inches by 5 inches. Its volume is 14×8×5=56014 \times 8 \times 5 = 560 cubic inches.

Section 2

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

Book overview

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

Continue this chapter

Chapter 7: Solve Area, Surface Area, and Volume Problems

  1. Lesson 1

    Lesson 1: Find Areas of Parallelograms and Rhombuses

  2. Lesson 2

    Lesson 2: Solve Triangle Area Problems

  3. Lesson 3

    Lesson 3: Find Areas of Trapezoids and Kites

  4. Lesson 4

    Lesson 4: Find Areas of Polygons

  5. Lesson 5

    Lesson 5: Represent Solid Figures Using Nets

  6. Lesson 6

    Lesson 6: Find Surface Areas of Prisms

  7. Lesson 7

    Lesson 7: Find Surface Areas of Pyramids

  8. Lesson 8Current

    Lesson 8: Find Volume with Fractional Edge Lengths