Guldin or it's not necessary? "surface" of revolution 3

Consider the single rectangle in $\mathbb{R}^2$that passes through the points $A = (1,2), B = (2,1), C = (4,3), D = (3,4)$旋转 $x$-axis in $\mathbb{R}^3$.

The volume of the surface of revolution obtained can be written as $A\pi \text{ unit}^3$.

Submit $A$.