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 ?

Solution (By Examveda Team)

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