To solve the given question, we need to understand the formula for the volume of a right pyramid, which is given by:
[tex]\[ V = \frac{1}{3} B h \][/tex]
where:
- [tex]\( V \)[/tex] is the volume of the pyramid,
- [tex]\( B \)[/tex] is a term we need to identify,
- [tex]\( h \)[/tex] is the height of the pyramid.
Let’s break this formula down step-by-step.
1. Volume Interpretation: The volume ([tex]\( V \)[/tex]) of any geometric shape is a measure of the space it occupies. For a pyramid, this involves both the base and the height.
2. Fraction Factor: The [tex]\(\frac{1}{3}\)[/tex] factor in the formula accounts for the fact that a pyramid has a volume that is one-third the volume of a prism that has the same base area and height.
3. Variable [tex]\( B \)[/tex]: The term [tex]\( B \)[/tex] accompanies the [tex]\(\frac{1}{3}\)[/tex] and height ([tex]\( h \)[/tex]). To determine what [tex]\( B \)[/tex] represents, observe how it interacts within the formula.
4. Role of Height ([tex]\( h \)[/tex]): Height ([tex]\( h \)[/tex]) is the perpendicular distance from the base to the apex of the pyramid.
By dimensional analysis, let’s check the units to deduce what [tex]\( B \)[/tex] should represent:
- [tex]\( V \)[/tex] (volume) is measured in cubic units (u³).
- [tex]\( h \)[/tex] (height) is measured in linear units (u).
In order for the right side of the equation, [tex]\(\frac{1}{3} B h\)[/tex], to result in cubic units:
[tex]\[ B \text{ must be in square units (u²) so that the product of } B \, (\text{u²}) \text{ and } h \, (\text{u}) \text{ results in cubic units (u³).} \][/tex]
So, [tex]\( B \)[/tex] must represent an area since only an area measurement will give us a [tex]\( u² \)[/tex] unit when multiplied by a length (height, [tex]\( h \)[/tex]).
5. Conclusion: The area of the base (usually represented by [tex]\( A \)[/tex] in many texts, but here [tex]\( B \)[/tex]) is the term that fits into the formula to satisfy the dimensional requirements and geometrical significance.
Therefore, [tex]\( B \)[/tex] represents the area of the base of the pyramid.
Answer: C. Area of the base
