Boxes are made by cutting 8cm squares from the corners of sheets of cardboard and then folding. The sheets of cardboard are 6cm lnbger than they are wide.
width of sheet= x
length of sheet = x+6
length of finished box = (x-10)
width of finished box = (x-16)
volume of the box = 8x^2-208x+1280cm^3
Find the dimensions of the sheet of cardboard needed to make a box with a volume of 1728cm^3.
so
8x^2 - 208x + 1280 = 1728
8x^2 - 208x - 448 = 0
x^2 - 26x - 56 = 0
(x-28)(x+2) = 0
x = 28 or x = -2, but x cannot be negative,
x = 28
the box is 12 wide, 18 long and 8 high
check: (12)(18)(8) = 1728
12444
a square piece of metal 18cm in each side n made a box without a top,by cutting a square from each corner folding up d flaps to form d side.what size corner should b cut in order volume of d box as large as possible?
It's not corret
To find the dimensions of the sheet of cardboard needed, we can use the volume equation for the box:
Volume of the box = 8x^2 - 208x + 1280 cm^3
Given that the volume of the box is 1728 cm^3, we can set up the equation:
1728 = 8x^2 - 208x + 1280
To solve this quadratic equation, we need to set it equal to zero:
8x^2 - 208x + 1280 - 1728 = 0
Simplifying the equation:
8x^2 - 208x - 448 = 0
Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. In this case, let's use factoring:
First, let's factor out any common factors:
8(x^2 - 26x - 56) = 0
Now, let's factor the quadratic expression inside the parentheses:
8(x - 28)(x + 2) = 0
Now we have two possible solutions:
x - 28 = 0 or x + 2 = 0
Solving these equations:
x = 28 or x = -2
Since the width of the sheet cannot be negative, we discard the solution x = -2.
Therefore, the width of the sheet of cardboard needed to make a box with a volume of 1728 cm^3 is 28 cm.