Final answer:
Rotating a square with a perimeter of 32 units around a line creates a cylinder, and the base circumference is approximately 25 units.
Step-by-step explanation:
The question asks what shape is created by the rotation of a square about a line and what the approximate circumference of the base would be if the square has a perimeter of 32 units. The square being rotated around a line will create a cylinder when the side of the square is the height and the rotation trace creates the circular base. To find the circumference of the base, we need to determine the diameter or radius of the circle that would fit within the square.
Given the perimeter of the square is 32 units, each side (a) is 32 units / 4 = 8 units. The diameter of the circle (2r) is equal to the side of the square, so the radius (r) is 8 units / 2 = 4 units. Using the formula for the circumference of a circle, C = 2πr, we can calculate the circumference as C = 2π(4 units) = 8π units. Since π is approximately 3.14159, the circumference is approximately 8 * 3.14159 = 25.13272 units, which can be rounded to about 25 units.