Learn on PengiBig Ideas Math, Course 1Chapter 8: Surface Area and Volume

Lesson 4: Volumes of Rectangular Prisms

In this Grade 6 lesson from Big Ideas Math Course 1, students learn how to find the volume of rectangular prisms with fractional edge lengths using the formulas V = Bh and V = ℓwh. Through hands-on activities, they explore how unit cubes can be subdivided to reason about fractional dimensions, then apply multiplication of fractions to calculate volumes. The lesson also introduces the formula V = s³ for cubes and connects volume concepts to real-world problems.

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 with Fractional Edge Lengths

Property

To find the volume of a real-world object shaped like a rectangular prism, multiply its length, width, and height. The dimensions can be whole numbers, fractions, or mixed numbers.

V=l×w×hV = l \times w \times h

Section 3

Finding a Missing Dimension

Property

When the volume and two dimensions of a rectangular prism are known, the missing dimension can be found by rearranging the volume formula: V=lwhV = lwh.
Solve for the unknown dimension by dividing the volume by the product of the known dimensions.

Examples

Book overview

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Chapter 8: Surface Area and Volume

  1. Lesson 1

    Lesson 1: Three-Dimensional Figures

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  2. Lesson 2

    Lesson 2: Surface Areas of Prisms

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  3. Lesson 3

    Lesson 3: Surface Areas of Pyramids

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  4. Lesson 4Current

    Lesson 4: Volumes of Rectangular Prisms

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Lesson overview

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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 with Fractional Edge Lengths

Property

To find the volume of a real-world object shaped like a rectangular prism, multiply its length, width, and height. The dimensions can be whole numbers, fractions, or mixed numbers.

V=l×w×hV = l \times w \times h

Section 3

Finding a Missing Dimension

Property

When the volume and two dimensions of a rectangular prism are known, the missing dimension can be found by rearranging the volume formula: V=lwhV = lwh.
Solve for the unknown dimension by dividing the volume by the product of the known dimensions.

Examples

Book overview

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

Continue this chapter

Chapter 8: Surface Area and Volume

  1. Lesson 1

    Lesson 1: Three-Dimensional Figures

    LearnPractice
  2. Lesson 2

    Lesson 2: Surface Areas of Prisms

    LearnPractice
  3. Lesson 3

    Lesson 3: Surface Areas of Pyramids

    LearnPractice
  4. Lesson 4Current

    Lesson 4: Volumes of Rectangular Prisms

    LearnPractice