Open-top boxes are constructed by cutting equal squares from the corners of cardboard sheets that measure 32cm by 28cm. Determine possible... dimensions of the boxes if each has a volume of 1920cm^3.
- print Print
- list Cite
Expert Answers
calendarEducator since 2011
write37 answers
starTop subject is Math
The first step to solving this problem is to create the equation. The volume of any open-top box is the length times width times height. Let the dimensions of the square being cut out of each corner of the rectangular cardboard be x by x. The length of the formed box will be (32-2x). The width will be (28-2x). The height will be x. The equation to solve becomes:
V=(32-2x)(28-2x)x
1920=(32-2x)(28-2x)x, or
(32-2x)(28-2x)x-1920=0
The equation can be solved by finding the zeros, x-intercepts, on a graph.
The graph shows that x=4, 6, or 20.
If x=4, then the length is 32-2(4)=24 cm, the width is 28-2(4)=20 cm and the height is 4 cm.
If x=6, then the length is 32-2(6)=20 cm, the width is 28-2(6)=16, cm and the height is 6 cm.
The value for x=20 is not possible since it would make the box edges negative.
Related Questions
- Open top boxes are constructed by cutting equal squares from the corners of sheets determine...
- 1 Educator Answer
- Find the maximum volume of an open box made from 3ft by 8ft rectangular piece of sheet metal by...
- 1 Educator Answer
- A box is to constructed from a sheet of cardboard that measure 3m x 5m. A square from each...
- 1 Educator Answer
- What should be the size of the squares cut so that the volume of the open box is maximum?if we...
- 1 Educator Answer
- A 6×6 sq. sheet of metal is made into an open box by cutting out a sq. @ each corner and then...
- 1 Educator Answer