If the radius increases by 10% then what will be the percent of increase in area?

Asked by rg_parmar | 7th Dec, 2014, 05:59: PM

Expert Answer:

L e t space t h e space r a d i u s space o f space t h e space c i r c l e space b e space r L e t space t h e space i n c r e a s e d space r a d i u s space b e space R G i v e n space t h a t space R over r equals fraction numerator 100 plus 10 over denominator 100 end fraction equals 110 over 100 equals 1.1 L e t space A subscript 1 space b e space t h e space a r e a space o f space t h e space c i r c l e space w i t h space r a d i u s space R T h u s comma space space A subscript 1 equals πR squared straight L straight e straight t space straight A subscript 2 space straight b straight e space straight t straight h straight e space straight a straight r straight e straight a space straight o straight f space straight t straight h straight e space straight c straight i straight r straight c straight l straight e space straight w straight i straight t straight h space straight r straight a straight d straight i straight u straight s space straight r straight T straight h straight u straight s comma space space straight A subscript 2 equals πr squared Now space consider space straight A subscript 1 over straight A subscript 2 equals πR squared over πr squared equals straight R squared over straight r squared equals open parentheses straight R over straight r close parentheses squared equals open parentheses 1.1 close parentheses squared over 1 equals 1.21 Thus comma space straight a space 10 % space increase space in space radius space is space equivalent space to space 21 % space increase space in space Area.

Answered by Vimala Ramamurthy | 8th Dec, 2014, 11:52: AM