The exterior surface of a cylinder with a circumference of 2 feet and a length of 5 feet (and no end caps) is the same as the area of
of a rectangle with width 2 and length 5.
To find the area of the exterior surface of a cylinder, we need to consider both the lateral surface area and the area of the two circular bases.
The lateral surface area of a cylinder is given by the formula:
Lateral Surface Area = circumference * height
In this case, the circumference of the cylinder is given as 2 feet, and the length or height is given as 5 feet. So, the lateral surface area is:
Lateral Surface Area = 2 (circumference) * 5 (height) = 10 square feet
The area of the circular bases of a cylinder is given by the formula:
Base Area = π * radius^2
Since the cylinder's circumference is given as 2 feet, we can find the radius using the formula for circumference:
Circumference = 2 * π * radius
Solving for the radius:
2 feet = 2 * π * radius
radius = 1 / π feet
Now, we can find the area of a single circular base:
Base Area = π * (1 / π)^2 = 1 square foot
Since the cylinder has two bases, the total area of the two bases is 2 square feet.
The exterior surface area of the cylinder is the sum of the lateral surface area and the area of the two bases:
Exterior Surface Area = Lateral Surface Area + 2 * Base Area = 10 square feet + 2 square feet = 12 square feet
Hence, the exterior surface of this cylinder with a circumference of 2 feet and a length of 5 feet is 12 square feet.