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Four congruent square pieces with lengths of sides of 6 cm were cut out of corners of a square piece of cardboard. Then this piece of cardboard was folded into an open-top box. Find the original dimensions of the piece of cardboard if the volume of the resulting box is 486 cm3.


100 + BRAINLIEST

Respuesta :

Let length be x

[tex]\\ \sf\longmapsto 6(x)(x)=486[/tex](V=lbh)

[tex]\\ \sf\longmapsto 6x^2=486[/tex]

[tex]\\ \sf\longmapsto x^2\dfrac{486}{6}[/tex]

[tex]\\ \sf\longmapsto x^2=81[/tex]

[tex]\\ \sf\longmapsto x=\sqrt{81}[/tex]

[tex]\\ \sf\longmapsto x=\pm 9[/tex]

Now side=

[tex]\\ \sf\longmapsto 9+6+6[/tex]

[tex]\\ \sf\longmapsto 9+12[/tex]

[tex]\\ \sf\longmapsto 21cm[/tex]

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