Answer :
Answer:
The length and width of the open box is 8 inches.
Step-by-step explanation:
Given : A machine produces open boxes using square sheets of metal. The machine cuts equal-sized squares measuring 4 inches on a side from the corners and then shapes the metal into an open box by turning up the sides. If each box must have a volume of 256 cubic inches.
To find : The length and width of the open box?
Solution :
Let the length and the width of the box be x as it is square shaped.
The machine cuts equal-sized squares measuring 4 inches on a side from the corners and then shapes the metal into an open box by turning up the sides.
Now, the side of the box cut 4 inches from both side
Length = x-8, Breadth = x-8 , Height = 4 inches
The volume of the box is 256 cubic inches.
The volume of the box is
[tex]V=l\times b\times h[/tex]
[tex]256=(x-8)\times (x-8)\times 4[/tex]
[tex]64=(x-8)^2[/tex]
[tex]x-8=8[/tex]
[tex]x=16[/tex]
Length of the box is x-8=16-8=8
Breadth of the box is x-8=16-8=8
Dimension of the box is [tex]8\times 8\times 4[/tex]
Therefore, The length and width of the open box is 8 inches.
Length = 8 inches
Width = 8 inches
- This is based on simple algebra.
- We are told that the sheet was square in shape and that equal sized squares of 4 inches were cut from the sides.
- Since this is formed into a box, it means the height will now be the length cut which is 4 inches.
Thus, height = 4 inches
- Now, since it is a square shaped plate with equal 4 inches cut from each corner, it means that the length and width will be equal. Let's call them both x.
- Now, we are told that the volume of the box is 256 in³.
- Formula for volume of a box is;
V = length × width × height.
Thus;
256 = x•x•4
4x² = 256
x² = 256/4
x² = 64
x = √64
x = 8
- Thus;
Length = 8 inches
Width = 8 inches
Read more at; brainly.com/question/13112783