# Maximise surface area of cuboid given constant volume.

• Feb 12th 2011, 05:50 PM
mandarep
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.
• Feb 12th 2011, 08:18 PM
mr fantastic
Quote:

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.