To find the volume of a right cone with a base area [tex]\(B\)[/tex] and height [tex]\(h\)[/tex], we use the standard formula for the volume of a cone.
A cone is a three-dimensional geometric shape that tapers smoothly from a flat base to a point called the apex or vertex. The formula for the volume [tex]\(V\)[/tex] of a right cone (a cone where the apex is directly above the center of the base) is derived as follows:
1. Formula for the volume of a cone:
[tex]\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \][/tex]
2. Substitute the given variables:
- Base Area = [tex]\( B \)[/tex]
- Height = [tex]\( h \)[/tex]
Thus, the formula for the volume of a right cone becomes:
[tex]\[ V = \frac{1}{3} B h \][/tex]
Therefore, the correct answer is:
A. [tex]\( V = \frac{1}{3} B h \)[/tex]
