If 2100 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box.

Volume(cubic centimeters) =

I got 20.4939015 and its wrong........

why doesn't ANYONE KNOW how to solve this.... :(

If you use BobPursley's answaer, you should get a cube with side length 20.493 cm for a and a^3 = 8607 cm^3 fr the volume

Recheck my previous posted answer. I found and corrected an error. I used calculus and got a somewhat higher volume.

http://www.jiskha.com/display.cgi?id=1283843608

THaNK YOU SO MUCH

To find the largest possible volume of the box, we need to consider the relationship between the length, width, and height of the box.

Let's assume the length of each side of the square base is 'x' cm. Therefore, the area of the square base will be x^2 square cm.

The height of the box will be 'h' cm.

The total surface area of the box consists of the area of the square base and the area of the remaining four sides.
The area of the square base is x^2 square cm, and the area of each of the four sides is x * h square cm. So, the total surface area is:
x^2 + 4(x * h) = x^2 + 4xh square cm.

According to the problem, we have 2100 square cm of material available, which is equal to the total surface area of the box.
x^2 + 4xh = 2100.

We'll solve this equation to find the value of 'h' in terms of 'x':
4xh = 2100 - x^2.
h = (2100 - x^2) / 4x.

Now, we need to find the volume of the box, which is given by the formula:
Volume = x^2 * h cubic cm.

Substituting the value of 'h' in the formula:
Volume = x^2 * (2100 - x^2) / 4x
= (x * (2100 - x^2)) / 4.

To find the maximum volume, we need to maximize this function. We can do that by taking the derivative with respect to 'x' and setting it equal to zero.

dV/dx = (2100 - 3x^2)/4 = 0.

Simplifying the equation:
2100 - 3x^2 = 0.

Now, solving for 'x':
3x^2 = 2100
x^2 = 2100 / 3
x^2 = 700
x = sqrt(700)
x ≈ 26.46 (rounded to two decimal places).

Substituting x back into the volume formula:
Volume = (x * (2100 - x^2)) / 4
= (26.46 * (2100 - (26.46)^2)) / 4
≈ 3086.76 cubic cm.

Therefore, the largest possible volume of the box is approximately 3086.76 cubic cm when the side length of the square base is approximately 26.46 cm.