What is the Volume of a Solid with Squares as Cross Sections?

[karush]

Let R be the region in the first quadrant bounded below by the graph of $y = x^2$ and above by the graph of
$y=x$. R is the base of a solid whose cross sections perpendicular to the x-axis are squares
\item What is the volume of the solid?
A 0.129
B 0.300
C 0.333
D 700
E 1.271ok I didnt understand what "square area" meant

 

[MarkFL]

I would first write:

$$dV=(x-x^2)^2\,dx=(x^2-2x^3+x^4)\,dx$$

Hence:

$$V=\int_0^1 x^2-2x^3+x^4\,dx=\frac{1}{30}$$

This seems to be none of the given choices.

 

[karush]

probably C 0.033 after adjusting the typo

so that was how the squares is implemented