The ratio of the curved surface area and the volume of a closed cylinder is 4:7.If its total surface area is 253 $$cm^{2}$$,then its height is:
(Taken $$\pi=\frac{22}{7}$$)

The ratio of the curved surface area and the volume of a closed cylinder is 4:7.

$$\frac{2\times\ \pi\ \times\ radius\times\ height}{\pi\ \times\ \left(radius\right)^2\times\ height}=\ \frac{4}{7}$$

$$\frac{2}{^{radius}}=\ \frac{4}{7}$$

$$\frac{1}{^{radius}}=\ \frac{2}{7}$$

radius = 3.5

If its total surface area is 253 $$cm^{2}$$.

total surface area of cylinder = $$2\times\ \pi\ \times\ radius\times\ \left(radius+height\right)$$

$$253 = 2\times\ \pi\ \times\ radius\times\ \left(radius+height\right)$$

$$253=2\times\ \frac{22}{7}\ \times\ 3.5\times\ \left(3.5+height\right)$$

$$23=2\times\ 2\ \times\ 0.5\times\ \left(3.5+height\right)$$

$$23=2\times\ \left(3.5+height\right)$$

height = 11.5-3.5

= 8