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IB MAI HL Calculus Topic 5.1 Differentiation (id: f7711e5f9)

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admin 发表于 2024-3-5 20:50:37 | 显示全部楼层 |阅读模式
本题目来源于试卷: IB MAI HL Calculus Topic 5.1 Differentiation,类别为 IB数学

[填空题]
A food company produces im. ofss ruz 35bm* , vzhx2bxr.as67ggqk*a00ce cre)fkx2oxad 0n5 hqc7i, ams in the shape of a cone with a hemisphere on top. Each ice cream consists of a cone base with height h and radius r, and a hemisphere on top of the cone's base, also with ac)hx2,7d kfonq x05ai radius of r. The total surface area of the ice cream cone is in cm$^2$ and is given by the formula
A=2$\pi$$r^2$+$\frac{60\pi}{r}$,
where r is the radius of the cone, in cm.

The ice cream designers of the company have been instructed to minimize the surface area of the cone in order to reduce the melting rate of ice cream.
1.Find $\frac{dA}{dr}$=a$\pi$r - $\frac{b\pi}{r^2}$.
a=  , b=  .
2.Calculate the value of r that minimizes the total surface area of the ice cream cone.
r=  cm.




参考答案:
空格1: 4空格2: 60空格3: 2.47±0.01


本题详细解析:

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