A growing circle: how fast does the area grow?बढ़ता हुआ वृत्त: क्षेत्रफल कितनी तेज़ी से बढ़ता है?Badhta hua circle: area kitni tezi se badhta hai?

NCERT Example 3 · Class 12 Maths · Chapter 6 · interactive diagram

Parts and what they mean

• Area A = \pi r^2 (क्षेत्रफल A = \pi r^2) — The area enclosed now, when the radius is r.
• Radius r (त्रिज्या r) — It changes with time t; its rate is \frac{dr}{dt} (4 cm/s in Example 3).
• Small increase dr (छोटी वृद्धि dr) — In a short time the radius grows by a little dr.
• Added strip (जुड़ी हुई पट्टी) — Its area is about (circumference) × dr = 2\pi r\,dr, so \frac{dA}{dt} = 2\pi r\,\frac{dr}{dt}.
• Centre O (केंद्र O) — Where the stone fell; the waves spread out from here.

Original diagram drawn by Simple Learning Hub, based on NCERT Example 3. Report a mistake