Open top boxes are constructed by cutting equal squares from the corners of sheets determine possible dimensions of the boxes if each has a volume of 1920cm3 The dimensions of the cardboard sheets are 32 cm by 28 cm

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Let us say the length of each side of the square to be x cm.

Then the volume of a box is `x^3`

Since we have open top boxes we need 5 squares to form one box.

Surface area of a box is `5x^2`

Volume of a box...

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Let us say the length of each side of the square to be x cm.

Then the volume of a box is `x^3`

 

Since we have open top boxes we need 5 squares to form one box.

Surface area of a box is `5x^2`

 

Volume of a box is given as `1920cm^3`

Therefore;

`x^3 = 1920`

   ` x = (1920)^(1/3) = 12.4289`

 

Let us say we have n number of boxes. Then the total area of the boxes are equal or marginally equal to the total surface area of the cardboard sheet.

`nxx5x^2 = 32xx28`

`nxx5xx12.4289^2 = 32xx28`

                         `n = 1.16`

 

Since the number of boxes cannot be a partial number number of boxes that can be created is 1.

 

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