The volume of a prism is the base [tex][tex]$(B)$[/tex][/tex] times the height [tex][tex]$(h)$[/tex][/tex]. Which of the following is the formula for the volume of a prism?

A. [tex][tex]$V=b w$[/tex][/tex]
B. [tex][tex]$V=B h$[/tex][/tex]
C. [tex][tex]$V=\frac{1}{2} B h$[/tex][/tex]
D. [tex][tex]$V=-B h$[/tex][/tex]



Answer :

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]