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.

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,

                               ......................(1)

                  Where, w - width

                                h - Height

                                l - length

                  From given, V= 486 cubic centimeters

                                        h = 6 cm ( Ref attachment)

                                       w = l

                  Equation (1) becomes,

                 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.    

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3