To determine the formula for the volume of a prism, we start by understanding the general principles of geometry related to prisms.
A prism is a solid object with two identical ends or bases and flat sides. The volume of a prism is given by the product of the area of its base and its height.
Let's denote the base area of the prism as [tex]\( B \)[/tex] and the height of the prism as [tex]\( h \)[/tex].
Given this information, we can establish that the volume [tex]\( V \)[/tex] of the prism can be calculated using the formula:
[tex]\[ V = B \times h \][/tex]
Thus, when we assess the given options:
A. [tex]\( V = b \times w \)[/tex]
- This is incorrect because it suggests multiplying two different dimensions unrelated to the height of the prism.
B. [tex]\( V = B \times h \)[/tex]
- This is correct. It accurately represents the volume of a prism as the area of the base multiplied by the height.
C. [tex]\( V = \frac{1}{2} B \times h \)[/tex]
- This is incorrect since dividing the product of the base area and height by 2 is irrelevant to the volume of a prism.
D. [tex]\( V = -B \times h \)[/tex]
- This is incorrect because the volume cannot be a negative value, and the formula does not represent the geometric principles correctly.
Therefore, the correct formula for the volume of a prism is:
[tex]\[ B. \; V = B \times h \][/tex]
