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varied directly math question

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發問:

the cost of painting a solid cylinder of radius r cm and height h cm varied directly as its total surface area. if r=4cm and h=6cm, the cost is $20. find the cost when r=8 and h=14. the ans. is 88 how can i get the answer? plz step by step thanks a lot!

最佳解答:

Total surface area: 2兀r2(the two circles)+2兀rh Let $C be the cost. C = k (2兀r2+2兀rh) C = k·2兀r(r+h) When r=4, h=6 and C=20, 20 = k·2兀(4)(4+6) k=1/4兀 .·.C=r(r+h)/2 When r=8 and h=14, C=8(8+14)/2 =88 .·.The cost is $88. :) 2012-08-31 13:44:55 補充： Sorry, I missed an important thing.. C = k (2兀r2+2兀rh), where k is a non-zero constant.

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