Final answer:
The correct formula to find the lateral area of a right cone, given the radius (r) and slant height (s), is C. LA=πrs. This formula is dimensionally consistent as it results in units of area, represented as length squared (L²).
option c is the correct
Step-by-step explanation:
The lateral area of a right cone (excluding the base) can be calculated using the formula LA = πrs, where r is the radius of the base and s is the slant height of the cone.
Therefore, the correct choice from the options provided is C. LA=πrs. This formula represents the lateral (side) surface area of the cone, which is the area of the cone's surface excluding its base.
The formula is derived from the sector of a circle, and when this sector is wrapped into the cone shape, the resultant surface is the cone's lateral area.
To understand why the formula is dimensionally consistent, we can consider each part of the equation. The dimension of area (A) is length squared (L²), so to be consistent, the formula should result in L² as well. In the formula LA = πrs, π (Pi) is a constant without dimensions, r (radius) has a dimension L (length), and s (slant height) also has a dimension L (length). Multiplying r and s gives us an expression with dimensions L², which is consistent with the dimensions for area. The dimensional analysis supports the correctness of the formula for lateral area of a cone.