A metal plate, with constant density 2 g/cm$^2$, has a shape bounded by the curve $y=x^2$ and the $x$-axis, with $0 \le x \le 2$ and $x,y$ in cm.

(a) Find the total mass of the plate.
mass =
(include units)

(b) Sketch the plate. Using your sketch, is $\overline x$ less than or greater than $1$?
A. less than
B. greater than

(c) Find $\overline x$.
$\overline x =$
(include units)