Geometric Solids

A geometric solid is any enclosed, three-dimensional object. The volume of a solid object describes how much space it contains. All geometric solids have a defined volume that can be calculated. One group of solids are called polyhedra. A cube is a special polyhedra called a regular hexahedron. It has six equivalent square sides all at right angles. The cube has a volume equal to the area of a side cubed. This is the reason taking a number to the power of three is called cubing. A pyramid is a solid with a polygonal base and triangles on all the other sides which meet at a point over the base. The volume of a pyramid is one-third times the area of the base times the height. A prism is a special solid with two congruent (equivalent) polygonal bases which are parallel to one another and the remaining faces are parallelograms. The volume of any prism is the area of the base polygon times the height. Other geometric solids that are not polyhedra include rounded objects such as a sphere which is ball shaped or a cylinder which is shaped liked a can. A sphere can be created by rotating a circle 180 degrees. The volume of a sphere is four thirds times the value of pi times the radius cubed. A cylinder can be created by moving a circle vertically. The volume of a cylinder is the height times the value of pi times the radius squared. Two inverted cones can be created in the three-dimensional geometric space by rotating an infinite line at a vertex point.

The volume of a cube:
y = x cubed,
where x is the area of each side.
If the area of each side is equal to 4,
then y is 4 cubed,
so the volume y = 64.

The volume of a sphere:
y = 4/3rds times pi times x cubed,
where x is the radius.
If the sphere has a radius of 3,
then y is 4/3rds times pi times 3 cubed,
so the volume y = 113.04.

The volume of a cylinder:
y = h times pi times x squared,
where x is the radius,
and h is the height.
If the cylinder has a radius of 3 and height of 5,
then y is 5 times pi times 3 squared,
so the volume y = 141.3.