Now I understand that the volume of a cuboid is V = whd but what I am struggling with is the following:
If w and d are both equal lets call them x, then how can I find an expression for h in terms of x? The closest I can get is
h = V / x^2
Is this correct?
In continuation how would I go about finding the surface area A in terms of x only using the answer from the first question?
Best Answer
Yes, that is correct.
The surface area of a cuboid with dimensions $w,h,d$ is $$A=2(wh+wd+hd)$$
This can be seen by computing the area of each of the faces of the cuboid and the adding them.
EDIT:
In your example, this reduces to $$A=2(xh+x^2+hx)=2x^2+4xh$$ Now, the question asks that you express this in terms of $x$ (not in terms of $x$ only) using the equation from the first question, i.e. $h=\frac{V}{x^2}$. So we substitute this expression for $h$ into the equation for the area to get $$A=2x^2+4x\frac{V}{x^2}=2x^2+4\frac{V}{x}$$