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,
[tex]Volume, V = whl[/tex]......................(1)
Where, w - width
h - Height
l - length
From given, V= 486 cubic centimeters
h = 6 cm ( Ref attachment)
w = l
Equation (1) becomes,
[tex]486=6(l^{2} )[/tex]
[tex]l^{2} = 81[/tex]
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.
