$\"\"$

The right circular cylinder is designed to hold soft drink of $\"\"$ .

(a)

Complete the table:

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

Radius $\"\"$	Height	Surface area $\"\"$
$\"\"$	$\"\"$	$\"\"$
$\"\"$	$\"\"$	$\"\"$
$\"\"$	$\"\"$	$\"\"$
$\"\"$	$\"\"$	$\"\"$
$\"\"$	$\"\"$	$\"\"$
$\"\"$	$\"\"$	$\"\"$

$\"\"$

(b)

Graph the surface area and label the minimum point:

$\"\"$

Using table feature of the graphing utility, complete the table:

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

Radius $\"\"$	Surface area $\"\"$
$\"\"$	$\"\"$
$\"\"$	$\"\"$
$\"\"$	$\"\"$
$\"\"$	$\"\"$
$\"\"$	$\"\"$
$\"\"$	$\"\"$
$\"\"$	$\"\"$
$\"\"$	$\"\"$
$\"\"$	$\"\"$
$\"\"$	$\"\"$

Observe the table:

The minimum surface area is $\"\"$ at $\"\"$ .

$\"\"$

(c)

Find the surface area $\"\"$ as a function of $\"\"$ .

The srface area $\"\"$ .

$\"\"$

(d)

Graph the surface area: $\"\"$ .

$\"\"$

Observe the graph:

The minimum surface area is $\"\"$ at $\"\"$ .

$\"\"$

(e)

The surface area is $\"\"$ .

Apply derivative on each side with respect to $\"\"$ .

$\"\"$

$\"\"$ .

Find the critical numbers by equating $\"\"$ .

$\"\"$

$\"\"$ .

Substitute $\"\"$ in $\"\"$ .

$\"\"$

$\"\"$ .

The radius is $\"\"$ and height is $\"\"$ .

$\"\"$

(a)

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

Radius $\"\"$	Height	Surface area $\"\"$
$\"\"$	$\"\"$	$\"\"$
$\"\"$	$\"\"$	$\"\"$
$\"\"$	$\"\"$	$\"\"$
$\"\"$	$\"\"$	$\"\"$
$\"\"$	$\"\"$	$\"\"$
$\"\"$	$\"\"$	$\"\"$

(b)

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

Radius $\"\"$	Surface area $\"\"$
$\"\"$	$\"\"$
$\"\"$	$\"\"$
$\"\"$	$\"\"$
$\"\"$	$\"\"$
$\"\"$	$\"\"$
$\"\"$	$\"\"$
$\"\"$	$\"\"$
$\"\"$	$\"\"$
$\"\"$	$\"\"$
$\"\"$	$\"\"$

The minimum surface area is $\"\"$ at $\"\"$ .

(c) The srface area $\"\"$ .

(d) Graph of $\"\"$ .

$\"\"$

Observe the graph:

The minimum surface area is $\"\"$ at $\"\"$ .

(e) The radius is $\"\"$ and height is $\"\"$ .