Chapter 4.3, Problem 55AYU

(a)

To determine

To Explain:

The total cost $C$ of the material as a function of the radius $r$ of the cylinder.

Answer to Problem 55AYU

The total cost of the material as a function of the radius $r$ of the cylinderis $C\left(r\right)=0.377r^2+\frac{40}{r}$ .

Explanation of Solution

Calculation:

  $\begin{array}{l}V=\pi r^{2}h=500\\ h=\frac{500}{\pi r^2}\\ C\left(r\right)=2\pi r^2\left(0.06\right)+2\pi r\left(\frac{500}{\pi r^2}\right)\left(0.04\right)\\ C\left(r\right)=37.7r^2+\frac{4000}{r}\\ C\left(r\right)=0.377r^2+\frac{40}{r}\end{array}$

(b)

To determine

To Graph:

  $C=C\left(r\right)$ using the graph and value of $r$ is the cost of $C$ a minimum

Answer to Problem 55AYU

The graph of $C=C\left(r\right)$ is

  

Explanation of Solution

Given Information:

  $C\left(r\right)=0.377r^2+\frac{40}{r}$

The graph of $C=C\left(r\right)$ is follows,

  $\begin{array}{l}C=C\left(r\right)\\ C\left(r\right)=0.377r^2+\frac{40}{r}\end{array}$