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)

Answer: Option A

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