Three dimensional figure

Question

describe the three dimensional figure formed by rotating a square around a line of symmetry?

Answer 1

Before rotating a square around a line of symmetry, it is best to see what happens when you rotate a square (2D figure) around one of its sides:

A great visualization of this can be found in Geogebra here: https://www.geogebra.org/m/UMHXAvhb#material/cJAqhUWm

1. To turn the rectangle into a square, make the height, h, and radius, R, (which is also the length of the rectangle) the same value, for example, h=2 and R=2.
2. To see the rotation of the square around its side, increase the t value (scrolling all the way to the right).

The 3-D figure formed is a cylinder with a radius of 2 and a height of 2.

Now think about how this is similar/different from when the square is rotated around a line of symmetry? For example the line of rotation will go straight down the middle of the square. In this case, you will still get a cylinder, however, the dimensions will be slightly different; the height of the cylinder will stay the same (2) but the radius will be half of the previous cylinder (1).