Area of a Circle
The formula for the area of a circle is:
A = area of circle
r = radius of circle
Since r = d/2 where d is the diameter of a circle, the formula for the area of a
circle in terms of its diameter is:
In describing plane shapes, you use only two dimensions: width and length;
there is no thickness. By adding the third dimension (thickness), you describe a
Consider the solids described below.
1. A PRISM is a figure whose two bases are polygons, alike in size and shape,
lying in parallel planes and whose lateral edges connect corresponding vertices and
are parallel and equal in length. A prism is a right prism if the lateral edge is
perpendicular to the base. The altitude of a prism is the perpendicular distance
between the bases.
2. A CONE is a figure generated by a line moving in such a manner that one
end stays fixed at a point called the vertex. The line constantly touches a plane
curve which is the base of the cone. A cone is a circular cone if its base is a circle.
A circular cone is a right circular cone if the line generating it is constant in length.
The altitude of a cone is the length of a perpendicular to the plane of the base drawn
from the vertex.
3. A PYRAMID is a figure whose base is a plane shape bounded by straight
lines and whose sides are triangular plane shapes connecting the vertex and a line
of the base. A regular pyramid is one whose base is a regular polygon and whose
vertex lies on a perpendicular to the base at its center. The altitude of a pyramid is
the length of a perpendicular to the plane of the base drawn from the vertex.
4. A CIRCULAR CYLINDER is a figure whose bases are circles lying in
parallel planes connected by a curved lateral surface. A right circular cylinder is
one whose lateral surface is perpendicular to the base. (Note: Any reference in this
text to a cylinder will mean a circular cylinder.) The altitude of a circular cylinder
is the perpendicular distance between the planes of the two bases.
COMMON VOLUME FORMULAS
All factors in the formulas must be in the same linear units. As an example
one term could not be expressed in feet while other terms are in inches.