Thread: 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



To maximize volume, we must have



or



Substituting this into our formula for , we have



To find the maximum volume, we note that since is differentiable everywhere and equals at the endpoints of its domain, it must attain a maximum at a point where .