The curved surface area of a cylinder is $3960 \, cm^{2}$ and its volume is $41580 \, cm^{3}$. Find the radius and height of the cylinder.

(N/A) Given for a cylinder:
Curved surface area $(CSA)$ $= 3960 \, cm^{2}$
Volume $(V)$ $= 41580 \, cm^{3}$
We know that:
$CSA = 2 \pi r h = 3960 \, cm^{2}$ --- $(1)$
$V = \pi r^{2} h = 41580 \, cm^{3}$ --- $(2)$
Dividing equation $(2)$ by equation $(1)$:
$\frac{V}{CSA} = \frac{\pi r^{2} h}{2 \pi r h} = \frac{41580}{3960}$
$\frac{r}{2} = 10.5$
$r = 21 \, cm$
Now,substitute $r = 21 \, cm$ in equation $(1)$:
$2 \times \frac{22}{7} \times 21 \times h = 3960$
$2 \times 22 \times 3 \times h = 3960$
$132 \times h = 3960$
$h = \frac{3960}{132} = 30 \, cm$
Thus,the radius is $21 \, cm$ and the height is $30 \, cm$.