Answer :

jacob193

Answer:

Approximately [tex]483.805\; {\rm cm^{2}[/tex].

Step-by-step explanation:

Let [tex]h[/tex] denote the height of this cylinder, and let [tex]r[/tex] 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, [tex]\pi\, r^{2}[/tex] each.
  • The area of the lateral surface: [tex](2\, \pi\, r)\, (h)[/tex], same as that of a rectangle with height equal to the height of the cylinder ([tex]h[/tex]) and width equal to the circumference of the circles at the top and bottom of the cylinder (radius [tex]r[/tex].)

The total surface area of this cylinder would be the sum of the area of these surfaces:

[tex]\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}[/tex].

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