To find the formula for the volume of a right cone with a given base area [tex]\( B \)[/tex] and height [tex]\( h \)[/tex], let's go through the steps and reasoning to determine the correct formula.
We start by recalling the standard formula for the volume of a cone. The volume [tex]\( V \)[/tex] of a cone is related to its base area [tex]\( B \)[/tex] and height [tex]\( h \)[/tex] through a specific mathematical relationship.
1. Volume Formula for a Cone: The volume of any cone (including a right cone) can be computed using the formula:
[tex]\[
V = \frac{1}{3} \times (\text{Base Area}) \times (\text{Height})
\][/tex]
2. Substitute the Given Variables: In the question, we are given that the base area is [tex]\( B \)[/tex] and the height is [tex]\( h \)[/tex]. So, substituting these values into the formula gives us:
[tex]\[
V = \frac{1}{3} \times B \times h
\][/tex]
3. Simplify: The formula simplifies to:
[tex]\[
V = \frac{1}{3} B h
\][/tex]
Now, let's compare this with each of the given options:
A. [tex]\( V = B h^2 \)[/tex]
B. [tex]\( V = \frac{1}{3} B h \)[/tex]
C. [tex]\( V = -\frac{1}{3} B h \)[/tex]
D. [tex]\( V = 3 B h \)[/tex]
From our derived formula, [tex]\( V = \frac{1}{3} B h \)[/tex], it is clear that the correct option is:
B. [tex]\( V = \frac{1}{3} B h \)[/tex].
