Total surface area of aright circular cylinder is 1848 cm$$^2$$. The ratio of its total surface area to the curved surface area is 3: 1. The volume of the cylinder is:(Take $$\pi = \frac{22}{7}$$)

We know that curved surface area = $$ 2\pi r h$$

total surface area = $$ 2 \pi r (r+h)$$

and volume of the cylinder = $$\pi r^2 h $$

according to question given ratio 

$$\Rightarrow \dfrac {2\pi r (r+h)}{2\pi r h} = \dfrac {3}{1}$$

$$\Rightarrow r +h = 3h $$

$$\Rightarrow 2h = r $$

then volume of cylinder =$$ \pi (2r)^2 h $$ = $$4\pi h^3 $$

given that $$2\pi r (r+h) = 1848 $$

$$\Rightarrow 2\pi \times 2h (3h) = 1848 $$

$$\Rightarrow 12\pi h^2 = 1848 $$

$$\Rightarrow \pi h^2 = 154 $$

$$\Rightarrow h^2 = \dfrac{154\times 7}{22}$$ = 49 

$$\Rightarrow h = 7 $$

then $$V = 4\pi h^3$$

$$\Rightarrow 4 \times \dfrac{22}{7}\times 343 $$

$$\Rightarrow 4312 cm^3 $$Ans