GMAT Exam: A Simple Guide To Geometry - Geometric Solids

Prisms and Pyramids
A prism is a solid with two congruent, parallel bases. A prism’s lateral faces are parallelograms.
(A lateral face is a side face.) In a right prism, the two bases are directly above each other and the lateral faces are rectangles.
The bases of a prism can have the shape of any polygon. Prisms are named according to the shape of their bases.
A cube is a right rectangular prism that has six congruent faces, all of which are squares.

Here is an example.


A pyramid is a solid with exactly one polygon-shaped base.
A pyramid’s lateral faces are triangles that meet at a point, called the apex.
In a right pyramid, the apex is directly above the center of the base.
The base can have the shape of any polygon.
Pyramids are named according to the shape of their bases.

Here is an example.


Cylinders and Cones
A cylinder has two parallel congruent bases, which are circles. In a right cylinder, the two bases are directly above each other.
A rectangular side wraps around and connects the two bases.


A cone is a three-dimensional solid that has one circular base and a single apex. In a right cone, the apex is directly above the center of the base.
A curved side wraps around to form the cone.


Spheres
A sphere is a three-dimensional solid that is shaped like a ball. Every point on its surface is the same distance from the center within the sphere.
The sphere’s radius is a line segment from the center of the sphere to any point on the sphere.
The sphere’s diameter is a line segment joining two points of the sphere and passing through its center.
The radius of the sphere is half the diameter. Equivalently, the diameter is twice the radius.