MTH 232
Section 10.5
Surface Area
Overview
• The surface area of a three-dimensional figure
is the sum of the area of all the polygons or
surfaces that make up, or comprise that
figure.
• Again, be reminded that area should be
expressed in square units.
• Finally, answers involving pi are
approximations if an approximation for pi
(3.14, 22/7, or your calculator’s pi key) is used.
Right Prism or Right Cylinder
SA  2 B  ph
Where B is the area of the base, p is the perimeter of the base, and h is the
height of the prism.
Right Regular Pyramid
1
SA  B  ps
2
Where B is the area of the base, p is the perimeter of the base, and
s is the slant height of the pyramid. Be prepared to have to use the
Pythagorean Theorem.
Right Circular Cone
SA  r  rs
2
Where r is the radius of the circular base and s is the slant height of the cone.
Again, be prepared to use the Pythagorean Theorem.
Sphere
S  4r
Where r is the radius of the sphere.
2
General Comments
• Sometimes the formulas for surface area can
be confusing. In some cases, it may be easier
to “deconstruct” the figures into its different
shapes, find the area of each one, then add
them together.
• This is especially helpful in the case of half
figures.
Examples
• 2(a); 2(d); 3(a); 3(c); 3(d); 4(d)