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Differential Calculus (id: 34310f39d)

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admin 发表于 2024-7-29 22:47:19 | 显示全部楼层 |阅读模式
本题目来源于试卷: Differential Calculus,类别为 IB数学

[填空题]
$\text { A closed cylindrical can with radius } r \mathrm{~cm} \text { and height } h \mathrm{~cm} \text { has a volume of } 24 \pi \mathrm{cm}^{3} \text {. }$


1. Express h in terms of r .   

The material for the base and top of the can costs 15 cents per $\mathrm{cm}^{2}$ and the material for the curved side costs 10 cents per $\mathrm{cm}^{2}$ . The total cost of the material, in cents, is C .
2. Show that C=30 $\pi r^{2}+\frac{480 \pi}{r}$ .   
3. Given that there is a minimum value for C , find this minimum value in terms of $\pi$ .   




参考答案:
空格1: 24/r^2空格2: 94.25*r^2+1507.96/r空格3: 1130.97±2%


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