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ICSE Class 8 Answered

A metal cylindrical disc of base radius 28cm and height 7 cm is melted and recact into a cylindrical block of radius 14 cm .find the length of the cylindrical block.also find the ratio of the total surface area of the cylindrical disc to that of the block.  
Asked by Kumaruday291936 | 22 Feb, 2019, 03:50: PM
answered-by-expert Expert Answer
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
Answered by Thiyagarajan K | 22 Feb, 2019, 04:35: PM
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