The surface area is the area that describes the material that
will be used to cover a geometric solid. When we determine the
surface areas of a geometric solid we take the sum of the area for
each geometric form within the solid.
The volume is a measure of how much a figure can hold and is
measured in cubic units. The volume tells us something about the
capacity of a figure.
A prism is a solid figure that has two parallel congruent sides
that are called bases that are connected by the lateral faces that
are parallelograms. There are both rectangular and triangular
To find the surface area of a prism (or any other geometric
solid) we open the solid like a carton box and flatten it out to
find all included geometric forms.
To find the volume of a prism (it doesn't matter if it is
rectangular or triangular) we multiply the area of the base, called
the base area B, by the height h.
A cylinder is a tube and is composed of two parallel congruent
circles and a rectangle which base is the circumference of the
The area of one circle is:
The circumference of a circle:
The area of the rectangle:
The surface area of the whole cylinder:
To find the volume of a cylinder we multiply the base area
(which is a circle) and the height h.
A pyramid consists of three or four triangular lateral surfaces
and a three or four sided surface, respectively, at its base. When
we calculate the surface area of the pyramid below we take the sum
of the areas of the 4 triangles area and the base square. The
height of a triangle within a pyramid is called the slant
The volume of a pyramid is one third of the volume of a
The base of a cone is a circle and that is easy to see. The
lateral surface of a cone is a parallelogram with a base that is
half the circumference of the cone and with the slant height as the
height. This can be a little bit trickier to see, but if you cut
the lateral surface of the cone into sections and lay them next to
each other it's easily seen.
The surface area of a cone is thus the sum of the areas of the
base and the lateral surface:
The volume of a cone is one third of the volume of a
Find the volume of a prism that has the base 5 and the height
Video lesson: Find the volume of a cone with
the height 5 and the radius 3.
Video lesson: Find the surface area of a
cylinder with the radius 4 and the height 8