The surface area of the cylinder is 602.88 square inches.
To find the surface area of a cylinder, we need to calculate the area of the two circular bases and the area of the curved surface.
Step 1: Calculate the area of the circular bases
The radius of the cylinder is half of the diameter, so the radius is 6 inches.
Use the formula for the area of a circle: A = πr².
Substitute the values: A = 3.14 × (6 inches)² = 3.14 × 36 square inches = 113.04 square inches.
Step 2: Calculate the area of the curved surface
The height of the cylinder is 10 inches.
The curved surface of a cylinder is like a rectangle that has been rolled into a cylinder.
The length of the rectangle is equal to the circumference of the circular base, which is 2πr.
The width of the rectangle is the height of the cylinder.
So, the area of the curved surface is A = 2πr × h = 2 × 3.14 × 6 inches × 10 inches = 376.8 square inches.
Step 3: Find the total surface area
Add the areas of the circular bases and the curved surface: Total surface area = 2 × area of circular bases + area of curved surface = 2 × 113.04 square inches + 376.8 square inches = 602.88 square inches.