I need help starting this problem...

[colin.wentz]

Determine the volume of the solid generated by extending the area bounded by the curves ? = ? 2 , ? = 3, and the x-axis into the z-direction so that each of the cross sections taken perpendicular to the x-axis are squares


-how do I start??

 

[blamocur]

Start by drawing the area in the XY plane.

 

[nasi112]

Let \(\displaystyle s\) be the length of one leg of the square, then the area of the square is \(\displaystyle s^2\).

The volume of one cross section is:
\(\displaystyle dV = s^2 \ dx\)

The total volume is:
\(\displaystyle V = \int dV = \int_a^b s^2 \ dx\)

From the given information, can you guess what are the values of \(\displaystyle a\), \(\displaystyle b\), and \(\displaystyle s\)?