List some objects from nature that resemble a circle.
Step-by-step solution
Idea: An object resembles a circle when its outline is (nearly) the same distance from one centre point all the way round. In nature this happens when something grows or spreads equally in every direction.
- In the sky: the full moon and the disc of the sun (we see the outline of a sphere, which is a circle).½ mark
- In water: ripples made by raindrops or a falling stone; a drop of water or dew seen from above.½ mark
- In plants: the cut face of a tree trunk or plant stem, a sunflower head, a slice of orange or lemon, the cap of a mushroom from above, a lotus leaf.½ mark
- In animals: the pupil and iris of an eye, the rings of a spider web (roughly), the cross-section of an earthworm.½ mark
- Why these are circular: each one grows or spreads out evenly from a centre, so every point of its edge is about the same distance from that centre.
Answer to write in the exam
Sky: full moon, disc of the sun
Water: ripples from raindrops, a dew drop seen from above
Plants: cut face of a tree trunk, sunflower head, slice of orange, mushroom cap (top view)
Animals: pupil and iris of an eye
∴ Each grows or spreads equally from a centre, so its edge is about the same distance from the centre all round.
Common mistakes that cost marks
- Listing man-made objects (a coin, a bangle, a wheel). The activity asks for objects from nature.
- Listing oval or egg shapes (an egg, a leaf, a mango). An oval is not a circle: its edge is not the same distance from the centre all round.
- Calling a solid object a circle: the Moon is a sphere; what looks like a circle is its outline.
How this can come in the exam
A circle is the set of all points in a plane that are
- at the same distance from a fixed line
- at the same distance from a fixed point
- inside a fixed square
- at less than a fixed distance from a fixed point
Show answer
(B) at the same distance from a fixed point
A circle is the set of points in a plane at a fixed distance (the radius) from a fixed point (the centre). Points at less than that distance fill the inside of the circle; they are not the circle itself.
Try one yourself
Is a slice of cucumber a circle, a cylinder, or neither? Explain.
Show answer
The cucumber itself is roughly a cylinder. A thin slice cut straight across has a face whose outline is (nearly) a circle, because the cucumber is equally thick in all directions from its middle.
More questions like this
- 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?
- 1. What are the rotational symmetries of a square? How many lines of reflection symmetry does it have? What about a regular pentagon? A regular hexagon?
2. What is the length of the longest chord in a circle of radius 5 units? Is there a smallest chord?
3. The locus of points at a given distance from a given point is a circle. What can we say about the locus of points equidistant from two given points?
(Hint: We know that any point that is equidistant from two given points A and B lies on the perpendicular bisector of AB. Does this make the perpendicular bisector the locus? For this, we have to show that all the points on the perpendicular bisector are equidistant from A and B.) - 1. How many circles pass through two points on a plane?
2. Are there circles of all possible radii passing through A and B? What is the radius of the smallest circle passing through A and B? What is the radius of the largest circle passing through A and B?
3. As you move away from segment AB along its perpendicular bisector, do the radii of the circles containing A and B increase or decrease?
4. As you go along the perpendicular bisector, will the circle drawn from that point through A and B appear more curved or less curved?
5. You are given two points A and B on a plane. How many squares can you draw on the same plane with A and B on the boundary? How many squares can you draw on the plane with A and B as the corners of the square?