# Thread: Maximise surface area of cuboid given constant volume.

1. ## Maximise surface area of cuboid given constant volume.

Hopefully this is the right section to be putting this ...
A cuboid tank is open at the top and the internal dimensions of its base are x m and 2x m. The height is h m. The volume of the tank is V cubic metres and the volume is fixed. Let S m^2 denote the internal surface area of the tank.
Find S in terms of x and h; and V and x.
State the maximal domain for the function defined by the rule in the above question.
If 2 < x < 15 find the maximum value of S if V=1000m^3.
Thank you.

2. Originally Posted by mandarep
Hopefully this is the right section to be putting this ...
A cuboid tank is open at the top and the internal dimensions of its base are x m and 2x m. The height is h m. The volume of the tank is V cubic metres and the volume is fixed. Let S m^2 denote the internal surface area of the tank.
Find S in terms of x and h; and V and x.
State the maximal domain for the function defined by the rule in the above question.
If 2 < x < 15 find the maximum value of S if V=1000m^3.
Thank you.
Surely you are familiar enough with the formulae for the volume and surface area of a cuboid to answer the first part ....? (And you can therefore get h in terms of V and x and so substitute into S)

Please show some effort here and say where you're stuck.