英语翻译Consider a container that is stored within thewall.The c
英语翻译
Consider a container that is stored within thewall.The container is formed as a sphere surmounted by a cone (like an icecream cone),the base of which is equal to the radius of the sphere.If theradius of the sphere is restricted to exactly 6ft and a surface area of 450 ft2is all that is allowed in the design（seethe following figure）,find the dimensions and such that thevolume of the container is a maximum.
Consider a container that is stored within thewall.The container is formed as a sphere surmounted by a cone (like an icecream cone),the base of which is equal to the radius of the sphere.If theradius of the sphere is restricted to exactly 6ft and a surface area of 450 ft2is all that is allowed in the design（seethe following figure）,find the dimensions and such that thevolume of the container is a maximum.
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大致意思是：
设想一个容器置于井中,容器形状由球形与圆锥形构成,圆锥底的半径为球形半径.如果球体半径为6ft,表面积（谁的?）为450ft2,为设计需求（如下图）,试确定各个尺寸,使得容器容积为最大.
看起来该物体由一个半球和一个圆锥（不完整?无锥顶?）组成,给定表面积,求最大容积的圆锥相关尺寸参数.但没有看到问题的附图,只能猜测.半球部分所有参数都是确定的.只有圆锥部分可能有变化（即圆锥为没有锥顶的一部分圆锥）.如此变成一个锥高与锥上部半径相关的函数,求其极值的问题.是否如此,看到图应该比较容易判断.
设想一个容器置于井中,容器形状由球形与圆锥形构成,圆锥底的半径为球形半径.如果球体半径为6ft,表面积（谁的?）为450ft2,为设计需求（如下图）,试确定各个尺寸,使得容器容积为最大.
看起来该物体由一个半球和一个圆锥（不完整?无锥顶?）组成,给定表面积,求最大容积的圆锥相关尺寸参数.但没有看到问题的附图,只能猜测.半球部分所有参数都是确定的.只有圆锥部分可能有变化（即圆锥为没有锥顶的一部分圆锥）.如此变成一个锥高与锥上部半径相关的函数,求其极值的问题.是否如此,看到图应该比较容易判断.
1年前 追问
8
题目好像说锥体的底面直径(base)等于球的半径r，可是那样的话x2不就固定了么。。。不懂
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