### Home > APCALC > Chapter 1 > Lesson 1.2.5 > Problem1-86

1-86.

A flag is defined by the region between the $x$-axis and:

$f ( x ) = \left\{ \begin{array} { c c c } { - x + 5 } & { \text { for } } & { 1 \leq x \leq 3 } \\ { 2 } & { \text { for } } & { 3 < x \leq 6 } \end{array} \right.$

Calculate the volume generated when the flag is rotated about the $x$-axis.

Sketch the flag. Since we do not know a geometric formula for the 3D figure that this flag will generate, subdivide it into familiar 3-D shapes:

What 3-D shapes will this generate? You should identify three.

a big cone $− a$ small cone $+ a$ cylinder

Use the eTool below to view the graph.
Click the link at right for the full version of the eTool: Calc 1-86 HW eTool