The radius of a cylinder is 5cm more than its height. If the curved surface area of the cylinder is 792 $$cm^2$$, then the volume of the cylinder (in $$cm^3$$​), is __________. [Use $$π = 22/7$$​]

Correct option is C

Given:

Curved surface area (CSA) = 792 cm²

radius, r = height(h) + 5.

​$$\pi = \frac{22}{7}.$$​

Formula Used:

Curved surface area(CSA) of cylinder = 2πrh

Volume of cylinder = πr²h

Solution:

From CSA:

​$$2\pi r h = 792 \\ \ \\ \Rightarrow \quad 2 \times \frac{22}{7} \times r \times h = 792$$​

$$r \times h = \frac{792 \times 7}{2 \times 22} = 126$$​​

Substituting r = h + 5:

​$$(h + 5) \cdot h = 126 \\ \ \\ \Rightarrow \quad h^2 + 5h - 126 = 0. \\ \ \\ h^2 + 14h - 9h - 126 = 0 \\ \ \\ h(h+14)-9(h+14)=0\\ \ \\ (h-9)(h+14) = 0 \\ \ \\ h = 9 \quad(h>0)$$​​

Now, 

r = h + 5 = 14 cm

So, Volume:

​$$\pi r^2 h = \frac{22}{7} \times 14^2 \times 9 = \frac{22}{7} \times 196 \times 9 = 5544 \, \text{cm}^3.$$​​