# [SOLVED]5.1.092 AP calculus Exam find area region

#### karush

##### Well-known member
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 1.271

ok I didnt understand what "squarea" meant

#### MarkFL

Staff member
I would first write:

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

Hence:

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

This seems to be none of the given choices.

#### karush

##### Well-known member
probably C 0.033 after adjusting the typo

so that was how the squares is implemented