This type of word problem involves the use of known formulas. Usually we used one of the formulas for either

volume or surface area, depending on what information was given, to solve for the radius, height, or slant

height of the cone. The

Pythagorean Theorem must often be used to find a missing radius, height, or slant height. It is necessary to remember that the

radius and

height always are legs and the slant

height always is the

hypotenuse of the right triangle. In one case, when both the

height and

surface area were given, we had to solve a

quadratic equation in order to determine the value of

*r*. If that

expression had not factored easily, we would have had to used the quadratic formula.