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 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 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 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 Where r is the radius of the sphere.

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)