If one of the diameters of the circle, given by the equation $x^2+y^2-4 x+6 y-12=0$, is a chord of a circle, ' S ', whose centre is at $(-3,2)$, then the length of radius of ' S ' is _______ units.

The area of the region bounded by the parabola $y^2=27 x$ and the line $x=1$ is ________ sq.units.

If $\sin (\alpha+\beta)=1, \sin (\alpha-\beta)=\frac{1}{2}, \alpha, \beta \in\left[0, \frac{\pi}{2}\right]$, then $\tan (\alpha+2 \beta) \cdot \tan (2 \alpha+\beta)=$

The value of $\int_0^\pi\left|\sin ^3 x\right| \mathrm{d} x$ is