Question

一道英文数学题，求具体步骤

An open cardboard box is to be make by cutting small squares of side x cm from each of the four corners of a larger square of card of side 10 cm, and folding along the dashed lines, as shown in the diagram. Find the value of x such that the box has a maximum volume, and state the value of that maximum volume.

（图片请大家自行想象，因为我实在是不会加图

Answer 1

Answer: 

           Because,It's volume=(10-2X)*(10-2X)*X

           So,According to the inequality:   Cube roots of ( abc)《(a+b+c)/3

                                 or :         abc《[(a+b+c)/3]³

                     When, and only when a=b=c ,Take equals

                    (10-2X)*(10-2X)*X= (10-2X)*(10-2X)*4X/4《[(10-2X+10-2X+4X)/3]³/4=(20/3)³/4

                            So,  (10-2X)*(10-2X)*X《2000/27

                     When (10-2X)=(10-2X)=4X

                             Solution of： X=5/3 

                       So ,When X=5/3 

                         The volume of the petitions cubes maximum is Vmax=2000/27

                (Inspection: ( 10-2*5/3)²*5/3=(5/3)*(20/3)²=2000/27)

                                                   《  End 》

Answer 2

可以用中文答吧？
将容积转化为x的函数就可以了，每个角去掉边长x的方形后，纸盒底为长10-2x的正方形，盒子的高为x，容积就好求了

解：由题意有容积V（x）=（10-2x）^2*x （0<x<5），即求V的最大值
(不知道你学导数没有，接下来需要用导数了）
V’=(10-2x)^2+2*(10-2X)*（-2）*x=(10-2x)(10-6x)
令V'=0，得x=5或5/3
有0<x<5，则x=5/3时，取得最值，此时V''<0,即为最大值
最大值V=2000/27