Here we have a cylinder without a base on the top (though still one on the bottom)
Let's break down the surface area of this cylinder.
[tex]SA_{cyl}=LA_{cyl}+B[/tex]
The surface area is equal to the lateral area plus the area of that one base.
The lateral area of any prism is equal to the perimeter of the base times the height.
[tex]LA=Ph[/tex]
In this case, since the base is a circle, the perimeter is the circumfrence, which can be found using C = 2πr...r = 4, so C = 8π. h = 7, so LA = 56π.
The base is just the area of a circle, which can be found with this formula.
[tex]A_\odot=\pi r^2[/tex]
r =4, so r² = 4×4 = 16, and the area of the base is = 16π.
SA = LA + B
SA = 56π + 16π
SA = 72π
