Final answer:
The student's question is about calculating the height of a cone when the volume and base radius are known. Using the volume formula for a cone, volume can be re-arranged to solve for the height, which involves substituting the known values into the rearranged formula.
Step-by-step explanation:
The question asks about finding the volume of a cone with a given base radius and volume. To find the height of the cone, we would typically use the formula for the volume of a cone, which is V = (1/3)πr²h, where V is the volume, r is the radius of the base, and h is the height. In this case, we know the volume (414.7 cubic inches) and the radius (6 inches), but we need to solve for the height (h).
To solve for h, we rearrange the formula to get h = (V × 3) / (π × r²). Substituting the given values, we have h = (414.7 in.³ × 3) / (π × 6 in.²). By performing the calculation, we can find the height of the cone. This height can be used to describe the dimensions of the cone or in further geometry problems involving the cone.