### Home > APCALC > Chapter 1 > Lesson 1.4.3 > Problem1-172

1-172.

A flag is defined by the region between the $x$-axis and the function listed below. Sketch the flag and calculate the volume of the solid generated by rotating the bounded region about the $x$-axis. To help you visualize this, use the 1-172 eTool (Desmos). Homework Help ✎
$f ( x ) = \left\{ \begin{array} { c c } { 2 } & { \text { for } 0 \leq x \leq 2 } \\ { 4 - x } & { \text { for } 2 < x \leq 4 } \end{array} \right.$

When rotated around the $x$-axis, it is a cylinder next to a cone, so volume is:

$V=\pi r^{2}h_{1}+\frac{1}{3}\pi r^2h_{2}$

Use the eTool below to visualize the flag.
Click the link at right for the full version of the eTool: Calc 1-172 HW eTool