Question

what is the formula for the surface area of a cylinder?

Answer 1

That will be the area of the top + area of the bottom plus the area of the side

Area of top and bottom is just the area of a circle with radius \(r\): \(A = \pi r^2\)
(don't forget you have 2 of those!)

Area of the side is the height of the cylinder times the circumference of the end. Think of it as a rectangle wrapped between two wheels. The length is the height, and the width is the distance around the wheel. \(A = (2\pi r) h\)

Add up the 3 quantities to get the total surface area of the cylinder in terms of \(r\) and \(h\).