Question

Find the surface area of the cylinder. __ cm squared.

Answer 1

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:

`\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}`

The area is 52π cm²