Question

TOPIC: General Application of Derivatives. Draw the necessary figure and indicate the dimension given

1. A closed cylindrical can is to have a volume of 130 cm³ and a minimum total surface area. Find the base radius R and the altitude H of the can.

Answer 1

volume:

$V=\pi R^2H$

surface area:

$A=2\pi R^2+2\pi RH=2\pi R^2+2\pi R\cdot \frac{130}{\pi R^2}=2\pi R^2+\frac{260}{ R}$

$A'(R)=4\pi R-\frac{260}{ R^2}=0$

$R=\sqrt[3]{\frac{65}{\pi}}=2.745$ cm

$H=\frac{V}{\pi R^2}=\frac{130}{\pi\cdot 2.745^2}=5.492$ cm