To determine the correct formula for the volume of a prism, let's start by understanding the given properties of a prism. The volume [tex]\( V \)[/tex] of a prism is defined as the product of the area of its base [tex]\( B \)[/tex] and the height [tex]\( h \)[/tex].
Let's examine each given option:
A. [tex]\( V = b w \)[/tex]
This equation suggests that the volume [tex]\( V \)[/tex] is the product of [tex]\( b \)[/tex] and [tex]\( w \)[/tex]. However, this does not align with the provided definition where the volume is derived from the base area [tex]\( B \)[/tex] and height [tex]\( h \)[/tex]. Therefore, option A is incorrect.
B. [tex]\( V = -B h \)[/tex]
This equation introduces a negative sign in the formula. The volume of a physical object like a prism cannot be negative as it represents a three-dimensional space. Therefore, option B is also incorrect.
C. [tex]\( V = \frac{1}{2} B h \)[/tex]
This option suggests that the volume [tex]\( V \)[/tex] is half of the product of the base area [tex]\( B \)[/tex] and height [tex]\( h \)[/tex]. However, the standard formula for a prism’s volume does not include this [tex]\( \frac{1}{2} \)[/tex] factor. This option is therefore incorrect.
D. [tex]\( V = B h \)[/tex]
This option directly matches the definition of the volume of a prism, where the volume [tex]\( V \)[/tex] is the product of the area of the base [tex]\( B \)[/tex] and the height [tex]\( h \)[/tex]. This formula is correct as it properly represents the relationship between the base area and height.
Given these considerations, the correct answer is:
D. [tex]\( V = B h \)[/tex]
