Question 5
Net of a sphere? Experiment and see if you can make a paper cutout that can perfectly wrap around a ball without leaving any wrinkles, gaps or overlaps.
A net is a flat shape that can be folded to make a 3D object.
Step 1 — Understanding Nets
A net is a 2D shape. We can fold it to make a 3D solid. Let us think of a cube. We can unfold a cube into a flat cross shape. This flat shape is the net of the cube. It covers the cube perfectly. There are no wrinkles, gaps, or overlaps.
Step 2 — The Sphere's Unique Shape
A sphere is a perfectly round 3D object. Its entire surface is curved. Imagine peeling an orange. The orange peel is curved. If we try to flatten the orange peel, it tears. Or it will wrinkle. We cannot flatten it without changing its shape. This is because a sphere's surface cannot be "unrolled" flat. It is different from a cube or a cylinder. A cylinder's curved side can be unrolled into a rectangle.
Step 3 — The Experiment and Conclusion
Let us try to make a paper cutout. We want it to wrap around a ball. We will find that it is impossible. No matter what shape we cut, it will wrinkle. Or it will leave gaps. Or it will overlap. This happens because paper is flat. A flat piece of paper cannot perfectly cover a curved surface. So, a sphere does not have a true net. We cannot make a perfect paper cutout.
Answer
(i) No, we cannot make a paper cutout that can perfectly wrap around a ball without leaving any wrinkles, gaps, or overlaps.
More questions in A
Build it in Your Imagination
We will start this section by practising visualisation. For each prompt, feel free to talk to your partner, gesture, draw it in the air — but do not actually draw on paper!
- Picture your name, then read off the letters backwards. Make sure to do this by sight, not by sound — really see your name! Now try with your friend's name.
Cut off the four corners of an imaginary square, with each cut going between midpoints of adjacent edges. What shape is left over? How can you reassemble the four corners to make another square?
Mark the sides of an equilateral triangle into thirds. Cut off each corner of the triangle, as far as the marks. What shape do you get?
Mark the sides of a square into thirds and cut off each of its corners as far as the marks. What shape is left?
Net of a sphere? Experiment and see if you can make a paper cutout that can perfectly wrap around a ball without leaving any wrinkles, gaps or overlaps.
Place an object in front of a plane, such as a wall of your room. Shine a torch light on the object in a direction perpendicular to the wall.
What do you see?
Observe what happens to the size of the shadow as you vary the distance between your torch and your object.
Context: Observe what happens to the size of the shadow as you vary the distance between your torch and your object.
Q. Why does this happen?
Construct a model of a cube and use your hands to keep it balanced on one corner vertex. Can you try to understand why all the projected edges have equal length?