To determine the correct formula for the volume of a prism, we need to understand how the volume of a prism is generally calculated.
1. Volume of a Prism:
The volume [tex]\( V \)[/tex] of a prism is given by the product of the area of its base [tex]\( B \)[/tex] and the height [tex]\( h \)[/tex] of the prism. This relationship can be expressed mathematically as:
[tex]\[
V = B \times h
\][/tex]
Here:
- [tex]\( B \)[/tex] represents the area of the base of the prism.
- [tex]\( h \)[/tex] represents the height of the prism.
2. Analyzing the Options:
Let's examine each given option to see which one matches the correct formula:
Option A:
[tex]\[
V = \frac{1}{2}Bh
\][/tex]
This formula resembles the area of a triangle, not the volume of a prism. So, this option is incorrect.
Option B:
[tex]\[
V = b w
\][/tex]
This formula might represent the area of a rectangle (where [tex]\( b \)[/tex] and [tex]\( w \)[/tex] are the base and width, respectively), not the volume of a prism. So, this option is also incorrect.
Option C:
[tex]\[
V = B h
\][/tex]
This formula matches our mathematical expression for the volume of a prism, [tex]\( V = B \times h \)[/tex]. Therefore, this option is correct.
Option D:
[tex]\[
V = -B h
\][/tex]
This formula introduces a negative sign, which does not make sense in the context of volume calculation. Hence, this option is incorrect.
3. Conclusion:
The correct formula for the volume of a prism is:
[tex]\[
V = B h
\][/tex]
Hence, the correct answer is:
[tex]\(\boxed{C}\)[/tex]
