Practical use of Calculus

15.1

A rectangular container has the following dimensions (cm)

Length $\displaystyle 3x $

Width $\displaystyle 90-3x $

depth $\displaystyle \frac{x}{3} $

Determine

15.1.1 Volume V in terms of $\displaystyle x$

15.1.2 The value for $\displaystyle x $ for which it has a max volume

15.2 The sum of two positive numbers x and y is 48

15.2.1 find y in terms of x

15.2.2 Prove that the sum of thier squares can be given by $\displaystyle 2x^3-96x+2304 $

15.2.3 Find the samllest possible value of the sum of thier squares

I have no idea >< I made a couple of attempts but it doesnt look right. weh!