For some surfaces, the normal lines at any point pass through the same geometric object. What is the common geometric object for a sphere? What is the common geometric object for a right circular cylinder? Explain.
every radius from the CENTER of a sphere hits the surface at a right angle.
For the cylinder that is not for the ends. The center works for the sides of the cylinder.
For a sphere, the normal lines at any point pass through the center of the sphere. The common geometric object for a sphere is a point.
To understand why this is the case, let's consider the definition of a normal line. A normal line to a surface at a given point is a line that is perpendicular to the surface at that point. In the case of a sphere, the surface is curved uniformly in all directions, which means that at any point on the sphere, the surface is perfectly symmetrical. Since a line that passes through the center of a sphere is perpendicular to the surface at any point on the sphere, it acts as the normal line for each of those points. Therefore, the common geometric object for a sphere is a point.
Now let's move on to a right circular cylinder. A right circular cylinder is a three-dimensional object with a curved surface that is formed by two parallel circular bases connected by a curved side. In this case, the normal lines at any point on the curved surface of the cylinder will be lines that are perpendicular to that curved surface.
However, unlike a sphere, the normal lines at different points on a right circular cylinder do not pass through the same geometric object. Instead, the normal lines at each point on the curved surface of the cylinder are distinct and perpendicular to that particular point on the surface. So, there is no common geometric object associated with the normal lines on a right circular cylinder.