Final answer:
To find Sandi's cone radius, use the lateral surface area of a cone excluding the base, given the material length and height. Solve for r using the formula by plugging in the height and solving the resulting quadratic equation.
Step-by-step explanation:
The question asks us to find the radius of a cone when given the total material in inches and the height of the cone. To solve for the radius, we need to use the formula for the surface area of a cone, which is usually given as A = πr2 + πrl, where A is the area, r is the radius, and l is the slant height. However, Sandi's cone uses material for the lateral (side) surface area only, so we will use the lateral surface area formula A = πrl. Since the total material is 338 inches, we have 338 = πr√(r2 + h2), where h is the height (6 inches).
To find the radius r, we can rearrange to 338/π = r√(r2 + 62). Squaring both sides yields (338/π)2 = r2(r2 + 36). This quadratic equation can be solved for r using algebraic methods, considering the physical constraints that the radius must be a positive real number.