Math, asked by Aadhyanathas, 4 months ago

a metal cylinder of base radius 6 cm and height 5 cm is melted and recast into a cylindrical bar of base radius 2 cm. Find the length of the bar formed.​

Answers

Answered by anandamvaishnav
4

Volume of cylinder of base radius r and length h = π×r2 × h  cm3

Total Surface area = 2π×r2+2π×r×h = 2πr×(r+h) cm2

 

Initial volume of metallic cylinder = π×28×28×7  ...........................(1)

 

after recasting with 14 cm radius and h cm length, volume = π×14×14×h  .......................(2)

 

since volume given by eqn.(1) and eqn.(2) are same,  length h of cylinder after recasting is given by,  h = begin mathsize 12px style fraction numerator straight pi cross times 28 cross times 28 cross times 7 over denominator straight pi cross times 14 cross times 14 end fraction space equals space 28 space c m end style

Ratio of total surface area = begin mathsize 12px style fraction numerator 2 straight pi cross times 28 cross times left parenthesis 28 plus 7 right parenthesis over denominator 2 straight pi cross times 14 cross times left parenthesis 14 plus 28 right parenthesis end fraction space equals space 5 over 3 end style

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