ICSE Class 10 Answered

$If space the space radius space of space straight a space sphere space increases space by space 10 percent sign space find space the space percentage space increase in space the space surface space area.$ Please provide solution to this question

Asked by Topperlearning User | 18 Oct, 2017, 02:49: PM

Expert Answer

$Let space the space radius space be space straight R. After space 10 percent sign space increase space new space radius space will space be space straight R plus fraction numerator 10 straight R over denominator 100 end fraction equals fraction numerator 11 straight R over denominator 10 end fraction Initial space surface space area equals 4 πR squared Changed space surface space area equals 4 straight pi open parentheses fraction numerator 11 straight R over denominator 10 end fraction close parentheses squared equals 4 straight pi 121 over 100 straight R squared Percentage space increase space in space area equals fraction numerator 4 straight pi 121 over 100 straight R squared minus 4 πR squared over denominator 4 πR squared end fraction cross times 100 equals fraction numerator begin display style 121 over 100 minus 1 end style over denominator 1 end fraction cross times 100 equals 21 percent sign$