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
Answer:
Volume of cylinder of base radius r and length h = πxr2 x h cm3
Total Surface area = 2mxr2+2πxrxh = 2nrx(r+h) cm2
Initial volume of metallic cylinder = nx28x28×7
.(1)
after recasting with 14 cm radius and h cm length, volume = Tx14×14xh
..(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
hope this was helpful