To find out what [tex]\(B\)[/tex] represents in the volume formula for a right pyramid, [tex]\( V = \frac{1}{3} B h \)[/tex], let's carefully analyze the components of the formula.
1. Understanding the Formula:
- [tex]\( V \)[/tex] represents the volume of the pyramid.
- [tex]\( \frac{1}{3} \)[/tex] is a constant factor in the formula, which indicates that the volume of a pyramid is one-third of the volume of a prism with the same base area and height.
- [tex]\( h \)[/tex] represents the height of the pyramid, measured as the perpendicular distance from the base to the apex (top point) of the pyramid.
- [tex]\( B \)[/tex] is the value we need to identify.
2. Breaking Down [tex]\(B\)[/tex]:
- The formula [tex]\( V = \frac{1}{3} B h \)[/tex] indicates that [tex]\(B\)[/tex] is a multiplier that directly affects the volume when combined with [tex]\(h\)[/tex]. For the entire formula to work dimensionally (i.e., the units on both sides of the equation must match those of volume), [tex]\(B\)[/tex] must involve a two-dimensional measurement.
3. Options Analysis:
- Option A: Area of the base
- If [tex]\(B\)[/tex] represents the area of the base, the formula correctly relates volume to a two-dimensional space (base area) and a one-dimensional height, providing the three-dimensional volume.
- Option B: Length of the base
- If [tex]\(B\)[/tex] represents just the length of the base, the dimensional analysis fails because length alone cannot combine with height to give a volume.
- Option C: Perimeter of the base
- If [tex]\(B\)[/tex] represents the perimeter of the base, again, dimensional analysis fails. The perimeter is a one-dimensional measure and cannot satisfy the volume correlation.
- Option D: Volume of the base
- If [tex]\(B\)[/tex] represents the volume of the base, it doesn't fit because the base itself is a two-dimensional figure and doesn't have volume.
Therefore, the correct interpretation of [tex]\(B\)[/tex] in the formula [tex]\( V = \frac{1}{3} B h \)[/tex] is:
Option A: Area of the base.
This means [tex]\(B\)[/tex] represents the area of the base of the pyramid.
