We have to calculate the surface of the cylinder.
We can list all the surfaces of the cylinder:
0. A top face that is a circle with radius r = 4 cm.
,
1. A base, which is equivalent to the top face.
,
2. A lateral face, that when developed is a rectangle of height h = 5 cm and width equal to the circumference of the base.
Then, we can calculate the surface area as the sum of these three areas:
[tex]\begin{gathered} A=A_1+A_2+A_3 \\ A=\pi r^2+\pi r^2+h\cdot C \\ A=2\pi r^2+h\pi r \\ A=2\pi(4)^2+5\cdot\pi(4) \\ A=2\pi\cdot16+20\pi \\ A=32\pi+20\pi \\ A=52\pi \end{gathered}[/tex]
The area is 52π cm²
