Final answer:
The surface area of a cylinder with radius x + 3 and height x + 11 is calculated using the formula A = 2πr² + 2πrh, leading to A = 4πx² + 40πx + 84π.
Step-by-step explanation:
To find the surface area of a cylinder with a radius of x + 3 and a height of x + 11, you can use the formula for surface area of a cylinder, which is A = 2πr² + 2πrh. This formula combines the areas of the two circular end-caps and the rectangular wrap which forms the curved surface area when rolled up.
Substituting the given radius and height into the formula gives us:
Upon expanding the terms, you will get:
Combining like terms, we find:
Therefore, the surface area of the given cylinder is 4πx² + 40πx + 84π, where π is approximately 3.1415927.