Question

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 cm^3.

Answer 1

The original dimensions of the cardboard is 21 cm × 21 cm, if a square pieces with lengths of sides of 6 cm were cut out of corners of a square piece of cardboard and the volume of the resulting box is 486 cubic centimeters.

Step-by-step explanation:

The given is,

                   Square pieces with lengths of sides of 6 cm were cut out of corners of a square piece of cardboard.

                  The volume of the resulting box is 486 cubic centimeters.

Step:1

                  The volume, is the given piece of cardboard was folded into an open box, we calculate side value of cardboard after cut into a square piece,

                  Formula for volume of cardboard is,

                               $Volume, V = whl$......................(1)

                  Where, w - width

                                h - Height

                                l - length

                  From given, V= 486 cubic centimeters

                                        h = 6 cm ( Ref attachment)

                                       w = l

                  Equation (1) becomes,

                                          $486=6(l^{2} )$

                                              $l^{2} = 81$

                 Take root on both sides

                                            l = 9 centimeters

Step:2

               Ref the attachment,

               Side value of piece of cardboard

                                                       = 6 + 9 + 6

                                                       = 21

               Side value of piece of cardboard = 21 centimeters          

               original sides of cardboard is 21 cm × 21 cm  

Result:

            The original dimensions of the cardboard is 21 cm × 21 cm, if a square pieces with lengths of sides of 6 cm were cut out of corners of a square piece of cardboard and the volume of the resulting box is 486 cubic centimeters.