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Unit 10 · Final Applications and ReviewLesson

Day 137Planning Storage and Packaging

LearnClassworkAnswer keyPDF packet ↗
Standards 6.G.A.26.G.A.4
LEARNING TARGET

I can connect volume and nets to compare storage designs.

01 · LEARN

Build the idea

Read the requested quantity first and identify the relevant model. 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. Explain why the units and the final value fit the situation.

WORKED EXAMPLE 1

Fill a prism 3/2 × 2 × 1 units with cubes of edge 1/2 unit. How many cubes fit? Use their volumes to verify lwh.

24 cubes; each 1/8 cubic unit; prism 3 cubic units

Counts along edges: 3, 4, 2. Product 24; 24 × 1/8 = 3, also lwh.

WORKED EXAMPLE 2

Draw a net for a triangular prism. Its two congruent right-triangle bases have legs 3 cm and 4 cm and hypotenuse 5 cm; prism length is 8 cm. Label all faces and find surface area.

2 triangles (area 6 each), rectangles 3×8, 4×8, 5×8; SA 108 cm²

Triangle pair: 12 cm²; rectangles: (3+4+5) × 8 = 96; total 108.

02 · PRACTICE

Your turn

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

  1. A rectangular prism has edges 7, 2, and 6 cm. Sketch it and find its volume.

  2. Fill a prism 5/2 × 7/2 × 2 units with cubes of edge 1/2 unit. How many cubes fit? Use their volumes to verify lwh.

  3. Draw a net for a closed 8 × 3 × 5 cm rectangular prism. Label the six faces and calculate total area.

  4. A 5 cm by 6 cm base and 5 cm height form a closed box. Draw its net and find the material area. Ignore tabs and overlap.

  5. A square pyramid has base edge 10 cm. Each triangular face has perpendicular face height 12 cm. Draw a net and calculate total surface area.

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

  7. Fill a prism 2/3 × 1 × 2 units with cubes of edge 1/3 unit. How many cubes fit? Use their volumes to verify lwh.

  8. Draw a net for a triangular prism. Its two congruent right-triangle bases have legs 3 cm and 4 cm and hypotenuse 5 cm; prism length is 2 cm. Label all faces and find surface area.

  9. A 8 cm by 7 cm base and 6 cm height form an open-top box. Draw its net and find the material area. Ignore tabs and overlap.

  10. A square pyramid has base edge 6 cm. Each triangular face has perpendicular face height 10 cm. Draw a net and calculate total surface area. Explain why the vertical pyramid height is not needed.

03 · CHECK

Answers and reasoning

Reveal the teacher answer key
  1. 84 cm³

    B = 7 × 2 = 14 cm²; V = B × 6 = 84 cm³.

  2. 140 cubes; each 1/8 cubic unit; prism 35/2 cubic units

    Counts along edges: 5, 7, 4. Product 140; 140 × 1/8 = 35/2, also lwh.

  3. 2 faces each of 8×3, 8×5, 3×5; 158 cm²

    Add 2(24) + 2(40) + 2(15) = 158.

  4. 170 cm²

    Closed surface area = 2(30+25+30) = 170.

  5. 340 cm²

    Base = 100; each triangle = 10 × 12 ÷ 2 = 60; add four triangles to get 340.

  6. 18 cm³

    B = 4 × 3/2 = 6 cm²; V = B × 3 = 18 cm³.

  7. 36 cubes; each 1/27 cubic unit; prism 4/3 cubic units

    Counts along edges: 2, 3, 6. Product 36; 36 × 1/27 = 4/3, also lwh.

  8. 2 triangles (area 6 each), rectangles 3×2, 4×2, 5×2; SA 36 cm²

    Triangle pair: 12 cm²; rectangles: (3+4+5) × 2 = 24; total 36.

  9. 236 cm²

    Closed surface area = 2(56+48+42) = 292. Remove the top area 56: 236.

  10. 156 cm²

    Base = 36; each triangle = 6 × 10 ÷ 2 = 30; add four triangles to get 156.

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