The ratio between the volume (in cm$$^3$$) and the curved surface area (in cm$$^2$$) of a cylinder is numerically 14 : 1. If the height of the cylinder is 50 cm, then what is the volume of the cylinder?(Take $$\pi = \frac{22}{7}$$)

The ratio between the volume (in cm$$^3$$) and the curved surface area (in cm$$^2$$) of a cylinder is numerically 14 : 1.

$$\frac{volume\ of\ a\ cylinder}{curved\ surface\ area\ of\ a\ cylinder}=\frac{\pi\ r^2\ h}{2\pi\ r\ h}\ =\ \frac{14}{1}$$

Here r = radius of cylinder and h = height of cylinder.

$$\frac{r^{ }\ }{2\ }\ =\ \frac{14}{1}$$

$$r=14\times2$$

r = 28 cm

If the height of the cylinder is 50 cm.
Volume of the cylinder = $$\pi\ r^2\ h$$

= $$\frac{22}{7}\times\left(28\right)^2\times50$$

= $$\frac{22}{7}\times784\times50$$

= $$22\times112\times50$$

= 123200 $$cm^3$$