0
$\begingroup$

A cylindrical package to be sent by a postal service can have a maximum combined length and girth (perimeter of a cross section) of 108 inches. Find the dimensions of the package of maximum volume that can be sent. (Assume the cross section is a circumference.)

My answer:

$$ \begin{align*} 2\pi \cdot r +h&= 108\\ V(r,h) &= \pi r^2 \cdot h \quad \Rightarrow \quad V(r) = \pi r^2 \cdot (108 - 2 \pi r)\\ \\ V'(r) &= 0 \quad \Rightarrow \quad -6\pi r^2+2\pi r \cdot 108 = 0 \end{align*} $$

since $ r \neq 0 $ we have $r = \dfrac{36}{\pi}$ and $h = 36$.

Is my reasoning ok?

Thank you.

  • 0
    Does "length and girth" mean the sum of the two? – 2017-01-24
  • 0
    Yes you are correct Andreas. I actually considered that on my calculations. Thank you. – 2017-01-24
  • 1
    There's another typo (squared $\pi$): it should be $-6\pi^2 r^2+2\pi r \cdot 108 = 0$. The following result is fine. – 2017-01-24

0 Answers 0