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From a 24-cm by 24-cm piece of cardboard, square
corners are cut out so that the sides can be folded up
to make a box. Complete parts a through c below.
a) Express the volume of the box as a function of the side x, in centimeters, of a cut-out square.



Answer :

mhanifa

Answer:

  • V(x)  =  4x³ - 96x² + 576x

Step-by-step explanation:

Cut out square on each corner has side of x.

When folded up the height of the box becomes same as the side of the cut-out square.

Sides  of the base of the box are:

  • 24 - 2x cm as it is folded on both sides.

The volume of the box which is the right square prism is:

  • V = Bh = a²h, where B- base area, a- side of the base, h- height.

Substitute the values and find the volume:

  • V(x)  = (24 - 2x)(24 - 2x)x = 4x³ - 96x² + 576x

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