Final answer:
The surface area of a cylinder with a circumference of 4 and height of 9 is approximately 119.38 square units, obtained by first calculating the radius from the circumference and then using the surface area formula with the calculated radius and given height.
Step-by-step explanation:
The question is asking about the surface area of a cylinder, which can be calculated if the cylinder's radius is known. However, the question provides the circumference of the cylinder. To find the radius (r), we use the formula C = 2πr, where C is the circumference. With a given circumference of 4, we can solve for the radius as follows:
r = C / (2π) = 4 / (2π) = 2 / π = 0.63661977...
Once we have the radius, we can calculate the surface area of the cylinder using the formula Surface Area = 2πrh + 2πr², where h is the height. The first term represents the area of the sides of the cylinder, and the second term represents the total area of the two ends (top and bottom). Since the height is given as 9, we substitute the values into the formula:
Surface Area = 2π(0.63661977...)(9) + 2π(0.63661977...)²
Calculating the surface area using the determined radius, we get:
Surface Area = 2π(0.63661977)(9) + 2π(0.63661977)² ≈ 36π + 2π ≈ 38π ≈ 119.38052...
So, the surface area of the cylinder is approximately 119.38 square units.