
What maximum volume?
USPS regulations require that any package must have length plus girth(distance around) of no more tha 84inches.Given this,what are the radius and height of a cylindrical package of maximum volume that is still mailable by parcel post?
I know we need to maximise this.But am stuck.Any suggestion?

We first state the problem in mathematical terms. Our formula for the volume of a cylinder is
$\displaystyle V=h\cdot\pi r^2.$
To maximize volume, we must have
$\displaystyle h+2\pi r=84$
or
$\displaystyle h=842\pi r.$
Substituting this into our formula for $\displaystyle V$, we have
$\displaystyle V=(842\pi r)\cdot \pi r^2.$
To find the maximum volume, we note that since $\displaystyle V$ is differentiable everywhere and equals $\displaystyle 0$ at the endpoints of its domain, it must attain a maximum at a point where $\displaystyle V'(r)=0$.