The radius of a cylinder is 5 m more than its height. If the curved surface area of the cylinder is 792 m2, what is the volume of the cylinder ?

Answer: Option C

Let the height of the cylinder be x cm
Then, radius = (x + 5) m
Curved surface area of the cylinder = $$2\pi rh$$
Now,
$$\begin{array}{rl}& 2\pi \left(x+5\right)\times x=792\\ & \Rightarrow 2\times \frac{22}{7}\times \left(x^2+5x\right)=792\\ & \Rightarrow x^2+5x=\frac{792\times 7}{44}=126\\ & \Rightarrow x^2+5x-126=0\\ & \Rightarrow x^2+14x-9x-126=0\\ & \Rightarrow x\left(x+14\right)-9\left(x+14\right)=0\\ & \Rightarrow \left(x-9\right)\left(x+14\right)=0\\ & \therefore x=9,-14\text{(neglect negative value)}\end{array}$$
∴ Height of cylinder = 9 m
∴ Radius of cylinder = 9 + 5 = 14 m
Volume of cylinder :
$$\begin{array}{rl}& =\pi r^{2}h\\ & =\frac{22}{7}\times 14\times 14\times 9\\ & =5544m^3\end{array}$$