The sum of the radius of the base and the height of a cylinder is 55 cm. If the height of the cylinder mentioned above is 15 cm more than the radius of its base, then what is the curved surface area of this cylinder? [Use $$\pi = \frac{22}{7}$$]

Let's assume the radius and height of the cylinder is 'r' and 'h' respectively.

The sum of the radius of the base and the height of a cylinder is 55 cm.

r+h = 55    Eq.(i)

If the height of the cylinder mentioned above is 15 cm more than the radius of its base.

h = r+15    Eq.(ii)

Put Eq.(ii) in Eq.(i).

r+r+15 = 55

2r+15 = 55

2r = 55-15

2r = 40

r = 20 cm

Put the value of 'r' in Eq.(ii).

h = 20+15

h = 35 cm

Curved surface area of this cylinder = $$2\times\ \pi\ \times\ r\times\ h$$

= $$2\times\ \frac{22}{7}\times\ 20\times35$$

= $$2\times\ 22\times\ 20\times5$$

= $$44\times\ 100$$

= 4400 $$cm^{2}$$