Answer:
Approximately \(483.805\; {\rm cm^{2}\).
Step-by-step explanation:
Let \(h\) denote the height of this cylinder, and let \(r\) denote the radius. The surface area of the cylinder consist of the following parts:
- The area of the two circles- one at the top and one at the bottom, \(\pi\, r^{2}\) each.
- The area of the lateral surface: \((2\, \pi\, r)\, (h)\), same as that of a rectangle with height equal to the height of the cylinder (\(h\)) and width equal to the circumference of the circles at the top and bottom of the cylinder (radius \(r\).)
The total surface area of this cylinder would be the sum of the area of these surfaces:
\(\begin{aligned}& \underbrace{\pi\, r^{2}}_\text{top} + \underbrace{\pi\, r^{2}}_{\text{bottom}} + \underbrace{2\, \pi\, r\, h}_{\text{lateral}} \\ =\; & \pi\, (7\; {\rm cm})^{2} + \pi\, (7\; {\rm cm})^{2} + 2\, \pi\, (7\; {\rm cm})\, (4\; {\rm cm}) \\ \approx\; &483.805\; {\rm cm^{2}} \end{aligned}\).
