Chapter 8.3, Problem 44E

a.

To determine

To find : the volume of the column.

Answer to Problem 44E

The volume of the column is $s^{2}h$ .

Explanation of Solution

Given information : A square of side length $s$ lies in a plane perpendicular to a line $L$ . One vertex of the square lies on $L$ . As this square moves a distance $h$ along $L$ , the square turns one revolution about $L$ to generate a corkscrew-like column with square cross sections.

The volume of the column is just given by the area of the cross section times the height that means $s^{2}h$ .

The fact that the column rotates forming a helix, or corkscrew is irrelevant.

b.

To determine

To explain : what will the volume be if the square turns twice instead of once.

Explanation of Solution

Given information : A square of side length $s$ lies in a plane perpendicular to a line $L$ . One vertex of the square lies on $L$ . As this square moves a distance $h$ along $L$ , the square turns one revolution about $L$ to generate a corkscrew-like column with square cross sections.

The number of twists is still irrelevant.

The volume is still $s^{2}h$ .