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CBSE Class 9 Answered

if  slant height of a cone is changed by 10% while radius remains unchanged then the volume changes by

 

Asked by anshuman457biswas | 22 Jul, 2018, 02:55: PM
Expert Answer
begin mathsize 16px style Let space straight r space equals space 3 space cm comma space straight h space equals space 4 space cm space and space l space equals space 5 space cm space for space the space original space cone.
Volume space of space cone space equals space 1 third πr squared straight h space equals space 37.71 space cm squared
As space radius space will space remain space same space and space l space will space increases space by space 10 percent sign.
Increased italic space l space equals space 10 over 100 cross times 5 equals 0.5
l space equals space 5 space plus space 0.5 space equals space 5.5 space cm
straight r squared plus straight h squared equals l squared
straight h squared equals l squared italic space italic minus space straight r squared equals 5.5 squared minus 3 squared equals 21.25
straight h equals 4.61 space cm
Volume space of space this space cone space equals space 1 third πr squared straight h space equals space 43.46 space cm squared
Increased space volume space equals space fraction numerator 43.46 minus 37.71 over denominator 37.71 end fraction cross times 100 equals 15.24 percent sign end style
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