Question

What is the surface area of a cylinder with a height of 3 and a radius of 7?

Answer 1

Break up the problem into two parts:  1) find the surface area of the sides of the cylinder and 2) find the surface area of the top or bottom and multiply your result by 2.

Part 1:  Imagine that you cut the side of the cylinder parallel to its axis once and then open up this shape to form a rectangle.  The length of this rectangle is equal to the circumference of the cylinder times the height/length of the cylinder parallel to its axis:  A1 = 2 pi (7 units) (3 units), or 42 pi square units.

Part 2:  The total area of the two ends of the cylinder is 2 (pi [7 units]^2), or 98 pi square units.

Add these two areas together to get the total surface area of the cylinder.