If the volume and curved surface area of a cylinder are 616 m³ and 352 m² respectively, what is the total surface area of the cylinder (in m²)

Solution(By Examveda Team)

Volume of cylinder = $$\pi {r^2}h$$
∴ Curved surface area of cylinder = $$2\pi rh$$
$$\eqalign{ & \therefore \frac{{\pi {r^2}h}}{{2\pi rh}} = \frac{{616}}{{352}} \cr & \Rightarrow r = \frac{{2 \times 616}}{{352}} \cr & \Rightarrow r = 3.5\,m \cr} $$
∴ Volume of cylinder :
$$\eqalign{ & \Rightarrow \pi {r^2}h = 616 \cr & \Rightarrow \frac{{22}}{7} \times 3.5 \times 3.5 \times h = 616 \cr & \Rightarrow 11 \times 3.5 \times h = 616 \cr & \Rightarrow h = \frac{{616}}{{11 \times 3.5}} \cr & \Rightarrow h = 16 \cr} $$
∴ Total surface area of the cylinder :
$$\eqalign{ & = 2\pi rh + 2\pi {r^2} \cr & = 2\pi r\left( {h + r} \right) \cr & = 2 \times \frac{{22}}{7} \times 3.5\left( {16 + 3.5} \right) \cr & = 2 \times \frac{{22}}{7} \times 3.5\left( {19.5} \right) \cr & = 22 \times 19.5 \cr & = 429\,{\text{sq}}{\text{.m}} \cr} $$