To determine the formula for the volume of a right cone with base area [tex]\(B\)[/tex] and height [tex]\(h\)[/tex], we recall the general formula for the volume [tex]\(V\)[/tex] of a cone. A right cone is a cone where the line segment connecting the apex (tip) of the cone to the center of its base is perpendicular to the base.
The volume [tex]\(V\)[/tex] of a cone is given by:
[tex]\[ V = \frac{1}{3} \text{(Base Area)} \times \text{(Height)} \][/tex]
Given the problem, the base area is denoted by [tex]\(B\)[/tex] and the height is denoted by [tex]\(h\)[/tex]. Substituting these into the formula gives:
[tex]\[ V = \frac{1}{3} B h \][/tex]
Therefore, the correct formula for the volume of a right cone is:
A. [tex]\( V = \frac{1}{3} B h \)[/tex]
Thus, the correct choice is [tex]\( \boxed{A} \)[/tex].
