Given a right pyramid with base area [tex]$B$[/tex] and height [tex]$h$[/tex], what does [tex]$\frac{1}{3} B h$[/tex] represent?
A. Cross-sectional area
B. Cross-sectional volume
C. Surface area
D. Volume
Answer (2)
The volume of a pyramid is calculated using the formula: V = 3 1 B h , where B is the base area and h is the height.
Given the expression 3 1 B h , we recognize it as the volume of a pyramid.
Therefore, 3 1 B h represents the volume of the pyramid.
The final answer is: Volume
Explanation
Problem Analysis We are given a right pyramid with base area B and height h , and we need to determine what the expression 3 1 B h represents.
Volume Formula The volume of a pyramid is given by the formula: V = 3 1 × base area × height In our case, the base area is B and the height is h , so the volume is: V = 3 1 B h
Conclusion Comparing the given expression 3 1 B h with the formula for the volume of a pyramid, we can conclude that 3 1 B h represents the volume of the pyramid.
Examples
Understanding the volume of pyramids is useful in architecture and construction. For example, when designing a pyramid-shaped structure, knowing the base area and height allows you to calculate the volume of materials needed to build it. This helps in estimating costs and ensuring structural stability.
The expression 3 1 B h represents the volume of a pyramid. This is derived from the formula for the volume of a pyramid, which states that the volume is calculated as one-third of the base area multiplied by the height. Therefore, the correct option is D. Volume.
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