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NCERT Solutions for Class 9th Maths Chapter 5 Chapter opening — In-text Questions

Book page 92–93 Updated on2026-09-08

Q1.
Can you recognise the origin of the shapes in Fig. 5.1?
Answer

All three pictures in Fig. 5.1 come from nature, and in each of them the shape is a circle.

  • Left: raindrops striking still water. Each drop sends out a ripple that spreads outward at the same speed in every direction, so every point of the ripple stays at the same distance from the point where the drop fell — a circle.
  • Middle: the cross-section of a tree trunk (a plant stem). The growth rings are nearly circular, because the stem thickens outward by roughly the same amount all round.
  • Right: the head (inflorescence) of a sunflower. The florets are packed around a single centre, and the outer boundary is a circle.
Why it happens: whenever something grows or spreads equally in all directions from one point, the boundary it reaches is the set of points at a fixed distance from that point. That is exactly the definition of a circle. The cave painters of Gudahandi drew circles because nature kept showing them this shape.
Try This: the Moon and the Sun in Fig. 5.2 look circular too — they are spheres, and the outline of a sphere seen from far away is a circle.
Q2.
Activity: List some objects from nature that resemble a circle.
Answer

Any object that spreads out equally in all directions from a centre will look circular. A few from around us:

  • Ripples made by a stone dropped into a pond.
  • The full Moon, and the Sun during a total solar eclipse.
  • The annual rings on the cut end of a log; the cross-section of a bamboo or a sugarcane stem.
  • The face of a sunflower; the flat top of a lotus seed-pod.
  • Cross-sections of fruits — orange, lemon, tomato.
  • A raindrop resting on a leaf; a soap bubble seen from above.
  • The pupil and iris of an eye; the outline of a bird's nest.
Check it yourself: for each object, ask "is there one point inside from which every boundary point is the same distance?" If the answer is yes, the shape really is a circle; if not (a mango, an egg), it is an oval, not a circle.
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