I have a few questions.
1) If a sphere is intersected by a plane that contains the center of the sphere, what would it look like?
2) Can the intersection of a plane and cylinder be a triangle?
What is a hemisphere?
http://mathworld.wolfram.com/CylindricSection.html
Sure! I'd be happy to answer your questions.
1) If a sphere is intersected by a plane that contains the center of the sphere, the resulting shape would be a circle. This is because the plane, passing through the center of the sphere, would slice through the sphere in a way that creates a perfectly symmetric circular cross-section.
2) The intersection of a plane and a cylinder can indeed be a triangle. However, this is only possible if the plane intersects the cylindrical surface in a way that creates a triangular cross-section. For example, if the plane is positioned diagonally across the cylindrical surface, it can create a triangular shape where the base of the triangle is a chord on the cylindrical surface and the apex is the point where the plane cuts through the axis of the cylinder.
A hemisphere is half of a sphere. It is a three-dimensional shape that is obtained by cutting a sphere into two equal parts along a plane that passes through its center. The resulting shape resembles a half of a ball or a dome. A hemisphere has a flat circular base and a curved surface that meets at a point called the apex. It is often used in various applications, such as architectural design, astronomy, and engineering.
To learn more about cylindrical sections, you can follow the link you provided to MathWorld. It provides detailed information about different types of cylindrical sections and their properties.