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CBSE Class 10 Answered

A solid hemisphere is attached to the top of a cylinder having the same radii If the height of the cylinder were doubled (keeping the radii fixed)the volume of the entire system increased by 50%.By what %age would the volume increased if radii of both were doubled keeping the height fixed.  
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Asked by bharatupmanyu9027 | 17 Aug, 2019, 06:50: PM
answered-by-expert Expert Answer
Volume of the entire system = Volume of cylinder + volume of hemisphere
straight V equals πr squared straight h plus 2 over 3 πr cubed..... left parenthesis straight i right parenthesis
If space the space height space is space doubled comma
straight V subscript 1 equals πr squared 2 straight h plus 2 over 3 πr cubed equals 2 πr squared straight h plus 2 over 3 πr cubed
rightwards double arrow straight V plus straight V over 2 equals πr squared 2 straight h plus 2 over 3 πr cubed
rightwards double arrow fraction numerator 3 straight V over denominator 2 end fraction equals πr squared 2 straight h plus 2 over 3 πr cubed... left parenthesis ii right parenthesis
Subtracting space left parenthesis straight i right parenthesis space from space left parenthesis ii right parenthesis comma space we space have
straight V over 2 equals πr squared straight h
rightwards double arrow πr squared straight h equals 2 over 3 πr cubed space... space From space left parenthesis straight i right parenthesis
The space radius space is space doubled
rightwards double arrow straight V subscript 2 equals straight pi left parenthesis 2 straight r right parenthesis squared straight h plus 2 over 3 straight pi left parenthesis 2 straight r right parenthesis cubed
space space space space space space space space equals 4 πr squared straight h plus 16 over 3 πr cubed
space space space space space space space space equals 2 straight V plus 4 straight V equals 6 straight V
Increased space percent sign equals fraction numerator 6 straight V minus straight V over denominator straight V end fraction cross times 100 equals 500 percent sign
Answered by Renu Varma | 19 Aug, 2019, 10:50: AM
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