What is the surface area of a cylinder with base radius 3 and height 6? Either enter an exact answer in terms of pi or use 3.14 for pi and enter your answer as a decimal.

To calculate the surface area of a cylinder, we need to find the area of the two circular bases and the area of the rectangular side that wraps around the cylinder. The formula for the surface area (SA) of a cylinder is:\[SA = 2\pi r^2 + 2\pi rh\]where \(r\) is the radius of the base and \(h\) is the height of the cylinder.Given:- Radius \(r = 3\)- Height \(h = 6\)Step 1: Calculate the area of the two circular bases.The area of one circular base is \(\pi r^2\), so for two bases, it's \(2\pi r^2\).\[2\pi r^2 = 2\pi (3)^2 = 2\pi (9) = 18\pi\]Step 2: Calculate the area of the side (the lateral surface area).The lateral surface area is the circumference of the base times the height, which is \(2\pi rh\).\[2\pi rh = 2\pi (3)(6) = 2\pi (18) = 36\pi\]Step 3: Add the areas of the bases and the lateral surface to find the total surface area.\[SA = 18\pi + 36\pi = 54\pi\]So, the exact surface area of the cylinder in terms of \(\pi\) is \(54\pi\) square units.If we use \(\pi \approx 3.14\), then the surface area in decimal form is:\[SA = 54\pi = 54 \times 3.14 = 169.56\]Therefore, the surface area of the cylinder is \(169.56\) square units when using \(\pi \approx 3.14\).