the volume of a box (also called a rectan-
gular parallelepiped) is length times width
times height, or lwh;the volume of
a cube is all the sides acubed, or a^3.
What are lateral surface areas?
In many mathematical texts, the lateral
surface area(L.A.) is given along with—
or instead of—the surface area (S.A.).
This type of area is the surface area of a
three-dimensional figure, excluding the
area of any bases. In other words, the lat-
eral surfaces are the side faces (or sur-
faces) of a solid, or any face or surface
that is not a base (or bottom of a figure).
What are the surface area, lateral
area,and volumeof a sphere?
A sphere is a set of points equidistant from a central point (a center); a sphere in two
dimensions is a circle. In the case of a sphere, the lateral and surface areas are the
same; therefore, a sphere with a radius rhas a surface/lateral area of 4 πr^2 ; the volume
of a sphere is 4/3 πr^3.
What are geometric transformations?
Geometric transformations are rules that mean there is a one-to-one correspondence
between two sets of points in two figures. A geometric transformation changes the
plane or three-dimensional space. Each transformation can be defined by thinking
about where each point is “taken,” with a point said to be “taken to its image.”
One way to visualize a transformation is to think of expanding, shrinking, or mov-
ing one figure to get a second figure. Depending on the transformation, the image will
either be congruent (equal) to the original image (called the identity transformation),
similar but not necessarily equal, or will not resemble the original at all.
What are some transformationsin geometry?
A transformation that keeps a figure’s same shape and size, but moves it to a new loca-
tion, is called isometry. There are several common types of these transformations.
Dilatationis the only transformation that does not create equal figures. It means to
take a shape and make it larger or smaller, but keep the same proportions. In terms of
a circle, a dilatation creates another circle with the same center, also known as a con- 191
GEOMETRY AND TRIGONOMETRY
In this irregular prism shape, the lateral area equals
the perimeter of shape A multiplied by L, and the
surface area equals the lateral area plus two times
the area of shape A.