Geometry: Prisms, Spheres, Cylinders, Cones, and Pyramids

Study Notes

Geometry: Prisms, Spheres, Cylinders, Cones, and Pyramids

Geometry is the branch of mathematics concerned with shapes and their properties. It involves the study of points, lines, surfaces, angles, curves, solids, and transformations. In geometry, we often deal with special types of objects called geometric figures. Let's explore some common geometric figures: prisms, spheres, cylinders, cones, and pyramids.

Prisms

A prism is a three-dimensional shape with two parallel congruent bases connected by rectangular faces parallel to the bases. A regular prism has two identical congruent bases of congruent triangles, squares, pentagons, hexagons, etc., where edges perpendicular to the base meet at right angles and the other edges (called sides) form congruent rectangles.

Examples of Prisms

There are several examples of prisms, including:

Triangular prism: Two triangles as bases with congruent lateral faces.
Rectangle prism: Two rectangles as bases.
Pentagonal prism: Two different polygons as bases.

Spheres

A sphere is a three-dimensional object that has all points equidistant from its center. In other words, every point on a sphere lies a constant distance from the center point. Spheres can have various radii, depending on how far apart the points are from the center.

Cylinders

A cylinder is a three-dimensional figure with two parallel circular bases connected by a curved surface called a lateral face. One end of the cylinder is open, while the other may be open or closed.

Cones

A cone is a solid figure consisting of a circular base, any height above it, and a vertex above the base, which extends infinitely far into space. Each cross section of a cone parallel to the base is a circle.

Pyramids

Pyramids are three-dimensional figures with polygonal bases and triangular faces meeting at a point called the vertex. There are several types of pyramids, including triangular, rectangular, square, and pentagonal pyramids.