$\"\"$

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

(a)

Complete the table :

Cross section area of isosceles trapezoid is $\"\"$ .

Where

$\"\"$ and $\"\"$ are bases of isosceles trapezoid.

$\"\"$ is height of isosceles trapezoid.

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

Base $\"\"$	Base $\"\"$	Altitude	Area
$\"\"$	$\"\"$	$\"\"$	$\"\"$
$\"\"$	$\"\"$	$\"\"$	$\"\"$
$\"\"$	$\"\"$	$\"\"$	$\"\"$
$\"\"$	$\"\"$	$\"\"$	$\"\"$
$\"\"$	$\"\"$	$\"\"$	$\"\"$
$\"\"$	$\"\"$	$\"\"$	$\"\"$

$\"\"$

(b)

Draw a coordinate plane.

Graph the cross-sectional area $\"\"$ :

$\"\"$

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

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

Angle $\"\"$	Area
$\"\"$	$\"\"$
$\"\"$	$\"\"$
$\"\"$	$\"\"$
$\"\"$	$\"\"$
$\"\"$	$\"\"$
$\"\"$	$\"\"$
$\"\"$	$\"\"$
$\"\"$	$\"\"$

Observe the table :

The maximum cross-sectional area is $\"\"$ at $\"\"$ .

$\"\"$

(c)

Find cross-sectional area of isosceles trapezoid.

The cross-sectional area of isosceles trapezoid is $\"\"$ .

The cross-sectional area is $\"\"$ Where $\"\"$ .

$\"\"$

(d)

The cross-sectional area is $\"\"$ .

Differentiate with respect to $\"\"$ .

$\"\"$

Equate $\"\"$ to zero.

$\"\"$

$\"\"$ and $\"\"$ .

The critical points are $\"\"$ and $\"\"$ .

$\"\"$

At $\"\"$ .

$\"\"$

Second derivative the critical point $\"\"$ is negative so it is maximum.

At $\"\"$ .

$\"\"$

Therefore, the maximum exist at $\"\"$ .

$\"\"$

(e)

$\"\"$

Observe the graph :

The maximum cross-sectional area is $\"\"$ at $\"\"$ .

$\"\"$

(a)

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

Base $\"\"$	Base $\"\"$	Altitude	Area
$\"\"$	$\"\"$	$\"\"$	$\"\"$
$\"\"$	$\"\"$	$\"\"$	$\"\"$
$\"\"$	$\"\"$	$\"\"$	$\"\"$
$\"\"$	$\"\"$	$\"\"$	$\"\"$
$\"\"$	$\"\"$	$\"\"$	$\"\"$
$\"\"$	$\"\"$	$\"\"$	$\"\"$

(b)

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

Angle $\"\"$	Area
$\"\"$	$\"\"$
$\"\"$	$\"\"$
$\"\"$	$\"\"$
$\"\"$	$\"\"$
$\"\"$	$\"\"$
$\"\"$	$\"\"$
$\"\"$	$\"\"$
$\"\"$	$\"\"$

The maximum cross-sectional area is $\"\"$ at $\"\"$ .

(c)

The cross sectional area is $\"\"$ Where $\"\"$ .

(d)

The maximum occurs at $\"\"$ .

(e)

$\"\"$

The maximum cross-sectional area is $\"\"$ at $\"\"$ .