A parcel delievery service will not deliver a package unless the length plus girth (distance around) doesn't exceed 84 inches. What is the radius, length, and volume of the cylindrical package.

Question

A parcel delievery service will not deliver a package unless the length plus girth (distance around) doesn't exceed 84 inches.  What is the radius, length, and volume of the cylindrical package.

anonymous · Answer

Apparently I can't spell delivery.

anonymous · Answer

With the information given, it seems as though there isn't just one answer. There are many possible measurements for a cylindrical package with a circumference and length sum of less than 84 inches.

anonymous · Answer

Oh yes.

anonymous · Answer

It seems that I want the maximum package.

anonymous · Answer

That is a pretty important bit of information.

anonymous · Answer

Maximum volume?

anonymous · Answer

Yes volume, length and radius.  Essential it wants the max volume along with the values of the shape.

anonymous · Answer

Hmmm. Perplexing. I figured it out, but I'm not sure I can tell you why, but the maximum volume seems to be when the circumference is 2/3 of 84 (56) and the length is 1/3 of 84 (28).

r = 8.9126768131
circ = 56
length = 28
volume = 6987.5386215066

Maybe someone else has a better way of explaining it.

anonymous · Answer

I see where the numbers are coming from. Which is fine. I'll get an explanation from the math tutoring department tomorrow.