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 $\displaystyle s$?