To find the lateral area of a right cone, we need to consider the formula used in geometry. The lateral area (LA) of a right cone with radius [tex]\( r \)[/tex] and slant height [tex]\( s \)[/tex] is given by the formula.
To determine the correct formula among the given options, let's analyze each one:
A. [tex]\(\angle A = r s\)[/tex]
This formula simply multiplies the radius and the slant height without considering the circular component of the cone, so it’s not the correct formula for the lateral area of a cone.
B. [tex]\(L A = \pi r s\)[/tex]
This formula matches the known geometric formula for the lateral area of a right cone. It correctly includes the radius, the slant height, and the factor [tex]\(\pi\)[/tex], which relates to the circular base of the cone.
C. [tex]\(\angle A = \frac{1}{2} \pi r s\)[/tex]
This formula is not the correct formula for the lateral area of a cone because it includes an additional factor [tex]\(\frac{1}{2}\)[/tex] that is not part of the standard formula for the cone's lateral area.
D. [tex]\(\angle A = 2 \pi r s\)[/tex]
This formula incorrectly multiplies an additional factor of 2, which is not accurate for the lateral area of a cone.
Therefore, the correct answer is:
[tex]\[B. \, L A = \pi r s\][/tex]
Thus, the lateral area of a right cone where [tex]\( r \)[/tex] is the radius and [tex]\( s \)[/tex] is the slant height is given by the formula [tex]\( L A = \pi r s \)[/tex].
