maths問題 (錐體)－omckyyo的部落格

標題:

maths問題 (錐體)

發問:

If the value of the volume of a cone is equal to the value of the surface area of the cone, express r in terms of h. Hence, find the minimum value of the height of the cone. r=radius h=height 更新: 好心人解答下我...好急用更新 2: 非常好我計到 r = √[9h/(h-6)] li度唔知計完左所以一路唔明= = 更新 3: To mr_gary_cheung, for your idea, I think you are wrong at all. in my question, we have to find the minimum value, not maximum value SO, I think 7 is the answer of this question

最佳解答:

V = pi*r^2*h/3 A = pi*r^2 + pi*r*√(r^2+h^2) pi*r^2*h/3 = pi*r^2 + pi*r*√(r^2+h^2) rh/3 = r + √(r^2+h^2) rh/3-r = √(r^2+h^2) r^2*h^2/9+r^2-2r(rh/3) = r^2+h^2 r^2*h^2+9r^2-6r^2*h = 9r^2+9h^2 r^2*h^2-6r^2*h = 9h^2 r^2*h(h-6) = 9h^2 r^2 = 9h/(h-6) r = √[9h/(h-6)] for h > 6 So, the minimum value of the height of the cone = 7 2009-01-12 19:09:42 補充： To gary, there should be no max value for h as my answer holds for h > 6 in real number case.

其他解答:

To mr_gary_cheung, for your idea, I think you are wrong at all. in my question, we have to find the minimum value, not maximum value SO, I think 7 is the answer of this question 2009-01-12 19:13:01 補充：真係非常唔該哂聽日就考數學la(中3) 仲有少少唔明|||||To: 匿名, I would like to know... according to your answer, h=8 (for example), I can still have R... So, h=7 is not the maximum value.. Do my thinking has something wrong? I think we have to use dR/dH to find the max. H value, right?