Final answer:
The surface area of the cylindrical cardboard sleeve is approximately 62.83 square inches, calculated using the formula for the lateral surface area of a cylinder with the given diameter of 5 inches and height of 4 inches.
Step-by-step explanation:
The question involves finding the surface area of a cylindrical cardboard sleeve that is used for holding a hot coffee cup without burning fingers. To calculate the surface area of the cylindrical sleeve, we use the formula for the lateral (or side) surface area of a cylinder, which is ℓ times the diameter times the height. Since the diameter of the sleeve is given as 5 inches and the height is 4 inches, we first find the radius, which is half of the diameter, hence 2.5 inches.
The surface area (A) of the cylinder is then determined with the formula:
A = ℓdh
= ℓ × (5 inches) × (4 inches)
= ℓ × 20 square inches
= 62.83 square inches (using ℓ ≈ 3.14159)
Therefore, the surface area of the cardboard sleeve is approximately 62.83 square inches.