To solve the problem of finding the volume formula for a right cone with a base area [tex]\( B \)[/tex] and height [tex]\( h \)[/tex], let's walk through the concepts and reasoning required to determine the correct formula.
1. Understanding the Shape:
- A right cone with a circular base has a volume that is calculated using a specific geometric formula.
2. Volume Formula for a Right Cone:
- The volume [tex]\( V \)[/tex] of any cone is given by the formula:
[tex]\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\][/tex]
- Here, the base area is represented by [tex]\( B \)[/tex], and the height of the cone is [tex]\( h \)[/tex].
3. Applying the Given Information:
- We know the base area [tex]\( B \)[/tex] and the height [tex]\( h \)[/tex] of the cone.
- Substituting these values into the general formula for the volume of a cone:
[tex]\[
V = \frac{1}{3} \times B \times h
\][/tex]
4. Comparing with Given Options:
- Option A: [tex]\( V = \frac{1}{3} B h \)[/tex]
- Option B: [tex]\( V = \frac{1}{2} B h \)[/tex]
- Option C: [tex]\( V = B h \)[/tex]
- Option D: [tex]\( V = -\frac{1}{3} B h \)[/tex]
5. Identifying the Correct Formula:
- Based on the established geometric formula for the volume of a cone, the correct expression is:
[tex]\[
V = \frac{1}{3} B h
\][/tex]
- This matches option A.
Therefore, the correct formula for the volume of a right cone with base area [tex]\( B \)[/tex] and height [tex]\( h \)[/tex] is:
A. [tex]\( V = \frac{1}{3} B h \)[/tex]
