Can you recognise the origin of the shapes in the figure?
Step-by-step solution
Idea: Look at each picture and ask what in nature makes that shape. All three grow or spread out equally in every direction from a centre, which is exactly why they come out as circles.
- First picture: rings on a water surface. These are ripples made by raindrops falling on water. Each drop starts a wave that moves out at the same speed in every direction.½ mark
- Second picture: rings inside a cut log. This is the cross-section of a plant stem (tree trunk). The stem adds a new layer all round each year, so the rings are nearly circles.½ mark
- Third picture: a flower head packed with seeds and ringed by petals. This is the inflorescence (flower head) of a sunflower.½ mark
- What they share: each shape has a centre, and its edge is (nearly) the same distance from that centre all the way round. That is what makes a shape a circle.½ mark
Answer to write in the exam
Picture 1: ripples formed when raindrops fall on water
Picture 2: cross-section of a plant stem (tree trunk) showing growth rings
Picture 3: flower head (inflorescence) of a sunflower
∴ Each shape spreads out equally in all directions from a centre, so each is circular.
Common mistakes that cost marks
- Naming the object but not the circular part: for the log, the circle is the cross-section (the cut face), not the whole trunk, which is a cylinder.
- Calling every round object a circle. A circle is a flat figure; a ball or the Moon itself is a sphere. Only the shape we see (its outline) is a circle.
- Forgetting to say why the shape is circular: something spreading at the same rate in every direction from one point.
How this can come in the exam
Which of these shapes found in nature is not close to a circle?
- The ripples made by a stone dropped in still water
- The cut face of a tree trunk
- The outline of the full moon
- A single cell of a honeycomb
Show answer
(D) A single cell of a honeycomb
A honeycomb cell is a hexagon (six straight sides). The other three spread out equally in all directions from a centre, so they are circular.
Try one yourself
A stone is dropped into a still pond. Explain why the ripples form circles and not some other shape.
Show answer
The wave moves out from the point where the stone fell at the same speed in every direction. So at any moment every point of the ripple is the same distance from that point. A set of points all at the same distance from one point is a circle.
More questions like this
- What properties are common to all circles, big and small?
- List some objects from nature that resemble a circle.
- Jamuna has a circular piece of paper. She is trying to locate its centre. Amina gives her a suggestion. She follows the instructions and is thrilled to find that it works. Can you guess what Amina told her?
- Say you are looking at a wheel of a vehicle. You see a point of the wheel touching the ground. When you look at the wheel again after some time, you again see a point of the wheel touching the ground. Can you tell if the two points are the same point?
- Draw a circle on the paper and cut along the circle. Fold the circular paper so that the boundaries overlap, then open it. You see a crease; it is a line of reflection symmetry of the circle. Does this line pass through the centre of the circle?