If 10,800 cm2 of material is available to make a box with a square base and an open top, find the largest possible volume of the box.

Question

anonymous · Answer

now this you need calc for

anonymous · Answer

put base at x, height as h and so you know that 

$$x^2+4xh=10800$$
$$h=\frac{10800-x^2}{4x}$$
$$V(x)=x^2h=x^2(\frac{10800-x^2}{4x})$$
$$V(x)=x\frac{10800-x^2}{4}=2700x-\frac{x^3}{4}$$

anonymous · Answer

now to find the max take the derivative, set = 0 and solve, get 
$$V'(x)=2700-\frac{3}{4}x^2$$
then 
$$2700-\frac{3}{4}x^2=0$$
$$\frac{3}{4}x^2=2700$$
$$x^2=3600$$
$$x=60$$

anonymous · Answer

how'd i do?

anonymous · Answer

$$\color{red}{\text{any typos my myininaya?}}$$

anonymous · Answer

hmmm i dont believe thats correct, satellite73.  My teacher says 60 is not the answer :/