Question
Sat March 07, 2015 By: Sanmit Ratnaparkhi

A right angled triangle whose sides are 3,4,5 cm revolved around its longest side find the TSA of figur so obtained.
 
Also i tend to do lots of calculation errors how should i avoid it until my exam and my exam is on tuesday

Expert Reply
Prasenjit Paul
Sun March 08, 2015
The space solid space is space rotated space about space the space side space AC comma space since space it space is space the space largest space side. We space know space BD perpendicular AC comma Let space DC equals straight x comma space AD equals 5 minus straight x BD equals straight r comma space the space radius space of space the space solid In space triangle ABD comma AB squared equals AD squared plus BD squared 4 squared equals left parenthesis 5 minus straight x right parenthesis squared plus straight r squared straight r squared equals 16 minus left parenthesis 5 minus straight x right parenthesis squared........ left parenthesis straight i right parenthesis In space triangle CDB comma CB squared equals CD squared plus BD squared 3 squared equals straight x squared plus straight r squared straight r squared equals 3 squared minus straight x squared........... left parenthesis ii right parenthesis Equating space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis comma 16 minus left parenthesis 5 minus straight x right parenthesis squared equals 3 squared minus straight x squared 16 minus 25 minus straight x squared plus 10 straight x equals 9 minus straight x squared 10 straight x equals 18 straight x equals 9 over 5 From space left parenthesis ii right parenthesis comma straight r squared equals 9 minus straight x squared straight r squared equals 9 minus open parentheses 9 over 5 close parentheses squared straight r squared equals 9 minus 81 over 25 straight r squared equals 144 over 25 straight r equals 12 over 5 CD equals 9 over 5 comma space AD equals 5 minus 9 over 5 equals 16 over 5 Radius space of space the space upper space and space lower space cones equals 12 over 5 Total space surface space area space of space the space upper space cone equals straight pi cross times 12 over 5 cross times 4 equals fraction numerator 48 straight pi over denominator 5 end fraction Total space surface space area space of space the space lower space cone equals straight pi cross times 12 over 5 cross times 3 equals fraction numerator 36 straight pi over denominator 5 end fraction Total space surface space area space of space the space whole space solid equals fraction numerator 48 straight pi over denominator 5 end fraction plus fraction numerator 36 straight pi over denominator 5 end fraction equals fraction numerator 74 straight pi over denominator 5 end fraction space cm squared
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