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Unit 08 · Area Volume and Surface AreaLesson

Day 113Base Area and Prism Volume

LearnClassworkAnswer keyPDF packet ↗
Standards 6.G.A.2
LEARNING TARGET

I can calculate prism volume with fractional edge lengths.

01 · LEARN

Build the idea

A rectangular prism has volume V = lwh = Bh, where B is base area. Fractional edge lengths still multiply. Use cubic units; surface area and volume measure different attributes.

WORKED EXAMPLE 1

A rectangular prism has edges 7, 3, and 2 cm. Sketch it and find its volume.

42 cm³

B = 7 × 3 = 21 cm²; V = B × 2 = 42 cm³.

WORKED EXAMPLE 2

A rectangular prism has edges 2, 2, and 3 cm. Sketch it and find its volume. Show both lwh and Bh.

12 cm³

B = 2 × 2 = 4 cm²; V = B × 3 = 12 cm³.

02 · PRACTICE

Your turn

Work in order. Start with the foundations, then build toward explanation and application.

  1. A rectangular prism has edges 3, 2, and 6 cm. Sketch it and find its volume.

  2. A rectangular prism has edges 4, 3 1/2, and 2 cm. Sketch it and find its volume.

  3. A rectangular prism has edges 8, 3, and 5 cm. Sketch it and find its volume.

  4. A rectangular prism has edges 2 1/2, 3, and 5 cm. Sketch it and find its volume.

  5. A rectangular prism has edges 1, 3, and 6 cm. Sketch it and find its volume.

  6. A rectangular prism has edges 3, 1 1/2, and 6 cm. Sketch it and find its volume.

  7. A rectangular prism has edges 2, 2, and 2 cm. Sketch it and find its volume. Show both lwh and Bh.

  8. A rectangular prism has edges 2, 1, and 3 cm. Sketch it and find its volume. Show both lwh and Bh.

  9. A rectangular prism has edges 2, 3, and 1 cm. Sketch it and find its volume. Show both lwh and Bh.

  10. A rectangular prism has edges 3, 2, and 2 cm. Sketch it and find its volume. Show both lwh and Bh.

03 · CHECK

Answers and reasoning

Reveal the teacher answer key
  1. 36 cm³

    B = 3 × 2 = 6 cm²; V = B × 6 = 36 cm³.

  2. 28 cm³

    B = 4 × 7/2 = 14 cm²; V = B × 2 = 28 cm³.

  3. 120 cm³

    B = 8 × 3 = 24 cm²; V = B × 5 = 120 cm³.

  4. 75/2 cm³

    B = 5/2 × 3 = 15/2 cm²; V = B × 5 = 75/2 cm³.

  5. 18 cm³

    B = 1 × 3 = 3 cm²; V = B × 6 = 18 cm³.

  6. 27 cm³

    B = 3 × 3/2 = 9/2 cm²; V = B × 6 = 27 cm³.

  7. 8 cm³

    B = 2 × 2 = 4 cm²; V = B × 2 = 8 cm³.

  8. 6 cm³

    B = 2 × 1 = 2 cm²; V = B × 3 = 6 cm³.

  9. 6 cm³

    B = 2 × 3 = 6 cm²; V = B × 1 = 6 cm³.

  10. 12 cm³

    B = 3 × 2 = 6 cm²; V = B × 2 = 12 cm³.

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