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reza is helping en shah to make a box without the top. the box is made by cutting away four squares from the corners of a 30cm square piece of cardbboard as shown in Figure 1 and bending up the resulting cardboard to form the walls of the box. find the largest possible volume of the box

 Jun 21, 2015

Best Answer 

 #1
avatar+118696 
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Let the squares that are cut out each be x by x cm       0<x<15

Now the volume of the prism will be

 

V=(302x)(302x)xV=x(900120x+4x2)V=4x3120x2+900xdVdx=12x2240x+900d2Vdx2=24x240$Stationarypointswilloccurwhen$dVdx=0 12x2240x+900=0x220x+75=0(x5)(x15)=0x=5orx=15

 

Whenx=5d2Vdx2=245240<0Maximumatx=5Whenx=15$Volumeis0$$Somaximumvolumeoccurswhenx=5$$Maximumvolume$=V=(3010)(3010)5=2000cm3

 Jun 21, 2015
 #1
avatar+118696 
+5
Best Answer

Let the squares that are cut out each be x by x cm       0<x<15

Now the volume of the prism will be

 

V=(302x)(302x)xV=x(900120x+4x2)V=4x3120x2+900xdVdx=12x2240x+900d2Vdx2=24x240$Stationarypointswilloccurwhen$dVdx=0 12x2240x+900=0x220x+75=0(x5)(x15)=0x=5orx=15

 

Whenx=5d2Vdx2=245240<0Maximumatx=5Whenx=15$Volumeis0$$Somaximumvolumeoccurswhenx=5$$Maximumvolume$=V=(3010)(3010)5=2000cm3

Melody Jun 21, 2015

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