Class 6 NCERT bridge course Answers Activity W2.4 Exploring Volume – Making a Triangular-Shaped Box

Activity W2.4: Exploring Volume – Making a Triangular-Shaped Box

 Discuss and Explore: 

1. Do the above activity by making a triangular shaped box and discuss your observations.

Activity W2.4: Exploring Volume – Making a Triangular-Shaped Box

Objective:

To explore how the shape of the base affects the volume of a box when using the same-sized sheet of paper. In this activity, students will make a triangular prism from the same-sized sheet used in Activity W2.3 and compare its volume with rectangular-based boxes.

 Materials Needed:

• 1 rectangular sheet of paper (same size as previous activity)

• Power tape or glue

• Ruler

• Grains or rice for measuring volume

• Empty container

 Procedure:

1. Take a rectangular sheet (e.g., 20 cm × 16 cm).

2. Fold or cut it to form a triangular prism box.

   • Fold the paper into a strip.

   • Roll or shape the cross-section into a triangle (e.g., equilateral or right-angled).

   • Tape or glue the edges securely.

3. Seal one end of the prism to make a base.

4. Pour grains/rice into the triangular box until full.

5. Pour the contents into a measuring container or another rectangular box made from the same paper.

6. Compare the amount of rice or volume occupied.

 A triangular prism made of paper

                                   

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Example Calculation:

Let’s assume:

• Base of triangle = 8 cm

• Height of triangle = 5 cm

• Length (height of prism) = 16 cm

Volume of triangular prism =

$$\text{Area of triangle} \times \text{Length} = \frac{1}{2} \times 8 \times 5 \times 16 = 320 \text{ cm³}$$

Compare with:

• Rectangular box from same paper = 640 cm³ (from W2.3)

• Triangular box = 320 cm³

The triangular box holds less than the rectangular box made from the same paper.

Discussion Questions:

1. Why do you think the triangular box holds less?
   Because the base of the triangle has less area than a rectangular base from the same paper.

2. How does the shape of the base affect volume, even with the same surface area?
    Shapes with broader or fuller bases (like rectangles) tend to enclose more volume than narrow ones (like triangles), assuming the same height.

3. What if you made a cylinder instead from the same paper? Would it hold more or less?
    You could explore this in the next activity!

Conclusion:

By folding the same-sized paper into different 3D shapes (rectangular, triangular), we observe that volume is influenced by the shape of the base. Even with identical surface area, design and folding technique can greatly impact how much a box can hold.