In order to determine who is correct, we need to clarify the components involved in calculating the surface area of a cone. The surface area (SA) of a cone can be calculated using the formula:
\[ SA = \pi r (r + l) \]
where:
- \( r \) is the radius of the base,
- \( l \) is the slant height of the cone.
Given the choices, let's analyze the statements:
- Claire is correct because 8 in. is the slant height of the cone. - This statement could be true if indeed 8 in. is the slant height.
- Claire is correct because 8 in. is the height of the cone. - If 8 in. is the height (not preferred for SA calculation directly, without slant height), this could also be potentially true.
- Miles is correct because 9 in. is the height of the cone. - This would also imply a different scenario, and might not be most useful for the formula without the slant height.
- Miles is correct because 9 in. is the slant height of the cone. - This could also be true if 9 in. is indeed the slant height.
Without further context about which measurements (8 in. or 9 in.) specifically refer to height or slant height, we can't definitively say who is correct. However, generally in geometry, the slant height plays a more direct role in determining surface area than just the vertical height.
If we assume that one of them is referring to the slant height and the other to the vertical height, the person referring to the slant height (which would be used in the formula) is the one who would be correct about calculating surface area.
Thus, without definitive designations of which measurements are what, we cannot conclusively determine who is correct unless we know the context.
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