Measures of Circles വൃത്തങ്ങളുടെ അളവുകൾ
How long a wire do you need to bend into a circle 5 cm across? How much ground does a round well cover? This chapter traps the circle between polygons with more and more sides, discovers that every circle's circumference is the same number of times its diameter – the famous π – and then finds its area, πr². An interactive, animated self-study guide: the basics from earlier classes, every idea of the chapter with real-life examples, animated solutions to every textbook question, a revision sheet, and a model test with a fully solved paper.
How to use this guide
🎬 Watch the animations
Polygons grow more sides, circles unroll and get cut into slices step by step. Press Next ▶ or ▶▶ Auto play.
🖐️ Play with the numbers
Sliders change radii and the number of sides – watch perimeters and areas creep towards the circle's.
✍️ Try before you see
Questions have a Show a hint button and a hidden final answer. Try first in your notebook.
📖 Textbook links
Purple മലയാളം words are the exact terms of your textbook (pages 151–164).
Learning path
Follow the pages in order. If you are confident with polygons, chords and Pythagoras, you may skim pages 1–4, but do try their quizzes.
The chapter in one picture
A regular polygon drawn inside a circle of diameter 1. As its sides increase, its perimeter comes closer and closer to the circle's circumference: a number a little over 3.14 that no fraction can name. Archimedes stopped at 96 sides; the slider goes there too.
Quick glossary (Malayalam ↔ English)
| Textbook term | English | Meaning |
|---|---|---|
| വൃത്തം / കേന്ദ്രം | Circle / centre | All points at the same distance from the centre |
| ആരം / വ്യാസം | Radius / diameter | Centre to edge r; edge to edge through the centre d = 2r |
| ചുറ്റളവ് | Circumference (perimeter) | Length around: c = πd = 2πr |
| പരപ്പളവ് | Area | Space inside: a = ½cr = πr² |
| ഞാൺ | Chord | A line joining two points of the circle |
| സമബഹുഭുജം | Regular polygon | All sides and all angles equal |
| വൃത്തവലയം | Ring (annulus) | The region between two circles with the same centre |
| വൃത്തഭാഗം | Part of a circle (sector, arc) | A slice or a piece of the edge |
| തോത് | Scale (proportion) | Double the diameter, double the circumference |
| π (പൈ) | Pi | Circumference ÷ diameter ≈ 3.1416 |
Made for self-learning. Works offline – every page is a single file. Study material prepared by Claude for Madhu's family study folder, October 2026.