Question

A large tank in the shape of a cuboid is to be made from a 54 m^2 of sheet metal. The tank has a horizontal base and no top. The height of the tank is x meters. The two of the opposite vertical faces are squares. Show that the volume, v m^3, of the tank is given by V = 18x - 2/3 x^3

Answer 1

Explanation:

Ok so what i've done so far is draw out a little version and realised that the square faces have a surface area of x² because they have a height of x and they are a square so it must be x² and as there are 2 squares I will have 2x².

If I just assume the long face is a then I would have ax and cause I have 3 faces in total (Minus the square faces) so that would leave me with 3ax.

So I have up to now 2x²+3ax = 54m²

Now would I rearrange to solve for a and leave it as 3ax = 54 - 2x² ?