To determine the correct formula for finding the lateral area (LA) of a right cone given the radius [tex]\( r \)[/tex] and the slant height [tex]\( s \)[/tex], let's review the properties and standard formula for the lateral area of a cone.
The lateral area of a right cone is the area of the cone's surface excluding its base. It is also known as the area of the "conical" part of the cone. The standard formula for the lateral area [tex]\( L_A \)[/tex] of a right cone involves the circumference of the base and the slant height.
Given:
- [tex]\( r \)[/tex] is the radius of the base of the cone.
- [tex]\( s \)[/tex] is the slant height of the cone.
The correct formula for the lateral area of a right cone is:
[tex]\[ L_A = \pi r s \][/tex]
Now, let's evaluate the provided options to see which one matches this standard formula.
A. [tex]\( L_A = \frac{1}{2} \pi r s \)[/tex]
This formula is incorrect because it has an unnecessary factor of [tex]\( \frac{1}{2} \)[/tex].
B. [tex]\( L_A = \pi r s \)[/tex]
This matches the standard formula for the lateral area of a cone and is therefore correct.
C. [tex]\( L_A = 2 \pi r s \)[/tex]
This formula is incorrect because it has an extra factor of 2.
D. [tex]\( L_A = r s \)[/tex]
This formula is incorrect because it does not include the [tex]\( \pi \)[/tex] constant.
Based on our review, the correct formula for finding the lateral area of a right cone is:
[tex]\[ \boxed{L_A = \pi r s} \][/tex]
