To determine who is correct about the dimensions needed to calculate the surface area of the cone, we need to know the roles of the height and the slant height in the surface area formula for a cone.
The formula for the surface area \( S \) of a cone is given by:
\[ S = \pi r (r + l) \]
where:
- \( r \) is the radius of the base of the cone,
- \( l \) is the slant height of the cone.
The height of the cone isn't used directly in calculating the surface area, but it could be related to the other dimensions if they described the cone in a context where the radius and/or slant height were derived from the height.
Given this:
- If Claire says that 8 in. is needed for the surface area calculation and it refers to the radius or the slant height, then she could be correct.
- If Miles says that 9 in. is needed and it refers to the slant height, then he could also be correct.
However, without additional context, it's impossible to definitively choose one person over the other as correct based solely on their provided dimensions. You would need to establish whether 8 in. refers to the radius or slant height, and likewise for Miles's 9 in.
Thus, if we assume:
- Claire uses 8 in. correctly as the radius,
- Miles uses 9 in. correctly as the slant height,
then both could be correct depending on which aspect of the cone's dimensions they are referring to. It's critical to clarify whether these measurements are the radius, height, or slant height and which dimension is needed for the calculation.
However, if you want to choose a single statement, you might lean towards the option that clarifies what is being used (either height or slant) based on their role in surface area calculation, i.e., "Miles is correct because 9 in. is the slant height of the cone" if 9 in. indeed refers to the slant height, since it is needed for the formula alongside the radius.
2 answers