To understand what [tex]\( B \)[/tex] represents in the volume formula for a right pyramid, let's carefully analyze the given formula:
[tex]\[ V = \frac{1}{3} B h \][/tex]
Here, [tex]\( V \)[/tex] stands for the volume of the pyramid, [tex]\( h \)[/tex] represents the height of the pyramid, and [tex]\( B \)[/tex] is the quantity we need to identify. The formula states that the volume [tex]\( V \)[/tex] is equal to one-third of [tex]\( B \)[/tex] times [tex]\( h \)[/tex].
To find what [tex]\( B \)[/tex] stands for, we consider the physical attributes that make up the volume of a pyramid.
1. Volume of a Right Pyramid: The volume is essentially how much three-dimensional space the pyramid occupies. For a pyramid, this is calculated with the factor [tex]\(\frac{1}{3}\)[/tex] because the pyramid is a solid that converges from a base to an apex point.
2. Height [tex]\( h \)[/tex]: The height of the pyramid is the perpendicular distance from the base to the apex.
3. Base: The shape of the base can vary; it can be a square, rectangle, triangle, or any polygon, and the properties of the base will directly influence the calculation of the volume.
Given these components, we recognize that volume is calculated by taking the area of the base and extending it through the height of the pyramid, then adjusting by the factor [tex]\(\frac{1}{3}\)[/tex].
Now, putting it all together:
- In the volume formula, [tex]\( V \)[/tex] (volume) is computed by multiplying the area of the base with the height, and then taking one-third of that product.
Thus, [tex]\( B \)[/tex] must be the term representing the area of the base of the pyramid.
So, the correct answer is:
A. Area of the base
