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 t

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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 t
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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 t
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

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 t

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]&sup3;

                     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]&sup3;/4=(20/3)&sup3;/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)&sup2;*5/3=(5/3)*(20/3)&sup2;=2000/27)

                                                   《  End 》

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