if a box has a width of 15, a height of 9 and a length of 18, what would be the least amount of cardboard needed to make the box
If no top:
If all from one rectangular sheet then:
length has to be 18+2*9
width has to be 15+2*9
I suppose you could say you save the four 9 by 9 corner cutouts, but not really.
If you make the bottom out of 15*18
and then the walls out of one long strip which is 9 *(2*18+22*15) then you save those wasted corners but have to use more corner tape.
if the top is included ...
SA = 2(15x9) + 2(15x18) + 2(9x18)
To calculate the least amount of cardboard needed to make the box, you need to find the surface area of the box. The surface area of a rectangular box is calculated by adding up the areas of all six sides.
Let's calculate the surface area step by step:
1. Start with the two largest sides, the front and back. The area of each is calculated by multiplying the width (15) by the height (9): Area of front/back = 15 * 9.
2. Next, calculate the area of the two smaller sides, the left and right. Both have a length (18) and a height (9): Area of left/right = 18 * 9.
3. Finally, calculate the area of the top and bottom of the box. Both have a length (18) and a width (15): Area of top/bottom = 18 * 15.
To get the total surface area, add up the areas of all six sides: Surface area = (2 * Area of front/back) + (2 * Area of left/right) + (2 * Area of top/bottom).
Substituting the above calculations into the formula:
Surface area = (2 * (15 * 9)) + (2 * (18 * 9)) + (2 * (18 * 15)).
Now, use these calculations to find the least amount of cardboard needed to make the box.