differentiation help

lavastar SG

A container, in the shape of a right pyramid with a square base, has a given surface area A. If the side of the base is of length x, prove that the volume V is given by 36V^2=(Ax)^2 -2Ax^4. Find the value of x for which V is maximum, and show that max value of V is (A^3/2) divide by sq root 288.

I have problem for proving the 1st part.. any help please? thanks

oOprinceOo SG

so chim i dont understand. wait for the pro to come Laughing

ispyyy SG

solution is as below :

http://mathworld.wolfram.com/SquarePyramid.html

eagle SG

if u know what a right pyramid is, you can easily do the brute force method

Find V in terms of x = 1/3 * 1/sqrt(2) * x^3
Find A in terms of x = (sqrt(3) + 1) x^2

Sub into equation and done

You can then easily differentiate to find x where V is max
and then sub x into equation and u get the final answer