Final answer:
To find the total surface area of the cylinder, calculate the area of the two circular bases and the lateral surface area. The total surface area of the cylinder is 192π square inches.
Step-by-step explanation:
To find the total surface area of the cylinder, we need to calculate the area of the two circular bases and the lateral surface area.
The circumference of the circle is given as 16π, which means the radius is 16π / (2π) = 8 inches.
The height of the cylinder is half the radius, so the height is 8 / 2 = 4 inches.
The area of each circular base is πr², which is π(8²) = 64π square inches.
The lateral surface area can be calculated by multiplying the circumference of the base by the height, which is 16π × 4 = 64π square inches.
The total surface area of the cylinder is the sum of the areas of the circular bases and the lateral surface area. So, the total surface area is 2(64π) + 64π = 192π square inches.