HAVE YOU EVER THOUGHT WHY CIRCLES HAVING RADIUS R HAVE AREA OF πR²
HOW IT'S DERIVED?
WHATS ITS DERIVATION
THINK FOR IT AT LEAST 15-20 MIN...............................
*********************************solution**************************************
WHAT IS CIRCLE??
For this derivation we neither use sector nor any integration Hence CIRCLE IS CONSIDERED AS COLLECTION OF RINGS OF DIFFERENT RADIUS TO MAKE A COMPLETE CIRCLE.
here we cut infinite rings hence the ring we are having only have length (HERE WE ASSUME WIDTH OF THE RING VERY VERY SMALL BECAUSE WE CUT INFINITELY MANY RING)
#PROOF
------> Here after cutting infinitely many e rings. We align them and it's look like we are arranging them in the order of right angle triangle having base = RADIUS OF CIRCLE and height=2πR(THAT IS THE LONGEST RING CUT OUT ALSO REFERRED AS CIRCUMFERENCE)
------> BY APPLYING AREA OF RIGHT ANGLE TRIANGLE = 1/2*BASE*HEIGHT=1/2*R*2πR=πR²
(HENCE PROVED)
THANKS
STAY TUNED WITH US
HAPPY LEARNING
