Find and interpret surface area of prisms and cylinders.
Add the circle tops and the wrapped side
Problem
Calculate the total surface area of a cylinder with radius \(4~\text{cm}\) and height \(7~\text{cm}\). Express the result in terms of \(\pi~\).
Big Picture
What this problem is really about
Inventory a closed cylinder as two circular bases plus one curved side. The bases contribute two copies of circle area, while unwrapping the side makes a rectangle whose length is the base circumference and whose width is the cylinder height. Add those contributions and retain pi for the requested exact surface area.
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