To solve the problem of identifying the correct expression for the area of the base ( [tex]\( B \)[/tex] ) of a cone, we need to recall that the base of a cone is a circle. Therefore, the area of the base should be the area of a circle.
Here are the given options for [tex]\( B \)[/tex]:
1. [tex]\( B = 1 \cdot W \)[/tex]
2. [tex]\( B = \frac{1}{2} \cdot b \cdot h \)[/tex]
3. [tex]\( B = \pi \cdot r^2 \)[/tex]
Let's analyze each option step-by-step:
1. Option 1: [tex]\( B = 1 \cdot W \)[/tex]
- This expression [tex]\( 1 \cdot W \)[/tex] is not related to the shape or area calculations of a cone's base. There is no common geometric interpretation for this expression as the area of a circle or any other relevant base.
2. Option 2: [tex]\( B = \frac{1}{2} \cdot b \cdot h \)[/tex]
- This expression corresponds to the area of a triangle, where [tex]\( b \)[/tex] is the base and [tex]\( h \)[/tex] is the height. Since the base of a cone is a circle, this formula is not applicable.
3. Option 3: [tex]\( B = \pi \cdot r^2 \)[/tex]
- This expression [tex]\( \pi \cdot r^2 \)[/tex] is the standard formula for the area of a circle, where [tex]\( r \)[/tex] is the radius. Since the base of a cone is indeed a circle, this is the correct expression for the area of the base of a cone.
After evaluating all the options, we can conclude that the correct formula for the area of the base [tex]\( B \)[/tex] of a cone is:
[tex]\[ B = \pi \cdot r^2 \][/tex]
Thus, the correct option is:
[tex]\[ \boxed{B = \pi \cdot r^2} \][/tex]
