Maths Calculus
posted by Daksh .
a sheet of cardboard is to be folded up to make a closed box. If the cardboard measures 55 cm by 80cm calculate the maximum volume of the box that can be made from this sheet of cardboard

Maths Calculus 
Reiny
let each side of the squares to be cut out be x cm
length = 802x
width = 552x , 0 < x < 27.5
height = x
V = x(802x)(552x)
= 4x^3 270x^2 + 4400x
dV/dx = 12x^2  540x + 4400
= 0 for a max of V
3x^2  135x + 1100 = 0
x = (135 ± √5025)/6
take it from there (I get x = appr 10.69)
Respond to this Question
Similar Questions

College Algebra
On a rectangular piece of cardboard with perimeter 11 inches, three parallel and equally spaced creases are made. The cardboard is then folded along the creases to make a rectangular box with open ends. Letting x represent the distance … 
geometry
On a rectangular piece of cardboard with perimeter 11 inches, three parallel and equally spaced creases are made. The cardboard is then folded along the creases to make a rectangular box with open ends. Letting x represent the distance … 
Maths  Algebra
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 = (x10) width … 
Calculus
A box with an open top is to be made from a square piece of cardboard by cutting equal squares from the corners and turning up the sides. If the piece of cardboard measures 12 cm on the side, find the size of the squares that must … 
Geometry
A box of cereal measures 8 inches high and 2 inches deep. If all surfaces are made of cardboard and the total amount of overlapping cardboard in the box is 7 square inches, how much cardboard is used to make the cereal box? 
Calculus
Squares with sides of length x are cut out of each corner of a rectangular piece of cardboard measuring 3 ft by 4 ft. The resulting piece of cardboard is then folded into a box without a lid. Find the volume of the largest box that … 
math
A sheet of cardboard measures 9 feet by 6 feet. Gina makes the entire sheet of cardboard into a closed box that is a perfect cube. What is the surface area of the box? 
Calc
You want to make a rectangular box, open at the top, by cutting the same size square corners out of a rectangular sheet of cardboard and then folding up the sides. The cardboard measures 10 in. by 12 in. What are the dimensions of … 
geometry
box of cereal measures 10 in .wide.12in . high, 3in deep .all surfaces made of cardboard and total overlapping cardboard in the box is 7in squared , how much cardboard is used to make a cereal box including the amount of overlapping … 
Maths
A gift box is made from a rectangular piece of cardboard that is three times as long as it is wide. 5 cm squares are cut from each corner and the ends are then folded up to make the box. If the box's volume is 4340 cm^3, find the length …