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ICSE Class 10 Answered

If the volume of a sphere is increased by 95.2%without changing the shape what will be the % increase in surface area
Asked by lovemaan5500 | 13 Jan, 2018, 03:09: PM
Expert Answer
begin mathsize 16px style Let space straight r space be space the space radius space of space the space original space sphere space and space straight R space be space the space radius space of space new space sphere. Volume space of space sphere equals 4 over 3 πr cubed Surface space area space equals straight S equals space 4 πr squared Volume space of space new space sphere equals straight V plus 95.2 percent sign space straight V 4 over 3 πR cubed equals straight V plus 952 over 1000 straight V 4 over 3 πR cubed equals 1952 over 1000 cross times 4 over 3 πr cubed straight R cubed equals 1952 over 1000 straight r cubed straight R equals cube root of 1952 over 1000 end root space straight r Surface space area space of space new space sphere equals 4 πR squared equals 4 straight pi open parentheses cube root of 1952 over 1000 end root close parentheses squared space straight r squared equals 4 straight pi open parentheses 1952 over 1000 close parentheses to the power of 2 over 3 end exponent space straight r squared Increase space in space surface space area equals 4 straight pi open parentheses 1952 over 1000 close parentheses to the power of 2 over 3 end exponent space straight r squared minus 4 πr squared equals 4 πr squared open square brackets open parentheses 1952 over 1000 close parentheses to the power of 2 over 3 end exponent space minus 1 close square brackets percent sign space increase space in space surface space area equals fraction numerator increse space in space surface space area over denominator Original space surface space area end fraction cross times 100 equals fraction numerator 4 πr squared open square brackets open parentheses 1952 over 1000 close parentheses to the power of 2 over 3 end exponent space minus 1 close square brackets over denominator 4 πr squared end fraction cross times 100 equals open parentheses 1952 over 1000 close parentheses to the power of 2 over 3 end exponent space minus 1 equals 56.19 percent sign end style
Answered by Sneha shidid | 15 Jan, 2018, 11:12: AM

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