The School of Sport Sciences (Tutor) Geometry Summer 2025
The volume of an oblique pyramid with a square base is [tex]$V$[/tex] units [tex]$^3$[/tex] and the height is [tex]$h$[/tex] units.
Which expression represents the area of the base of the pyramid?
A. [tex]$V$[/tex] units [tex]$^2$[/tex]
B. [tex]$(3V - h)$[/tex] units [tex]$^2$[/tex]
C. [tex]$(V - 3h)$[/tex] units [tex]$^2$[/tex]
D. [tex]$\frac{V}{3h}$[/tex] units [tex]$^2$[/tex]
Answer (2)
Recall the formula for the volume of a pyramid: V = 3 1 B h .
Solve the formula for the area of the base B in terms of the volume V and height h : B = h 3 V .
The area of the base of the pyramid is expressed as h 3 V .
The final answer is h 3 V .
Explanation
Problem Analysis We are given the volume V and height h of an oblique pyramid with a square base. We need to find the area of the base.
Volume Formula The formula for the volume of a pyramid is given by: V = 3 1 B h where V is the volume, B is the area of the base, and h is the height.
Solving for Base Area We need to solve for B in terms of V and h . Multiplying both sides of the equation by 3, we get: 3 V = B h Now, divide both sides by h :
B = h 3 V
Final Answer Therefore, the area of the base of the pyramid is h 3 V units 2 .
Examples
Understanding the volume of pyramids is useful in architecture and construction. For example, if you know the volume and height of a pyramid-shaped structure, you can calculate the area of its base to determine the amount of material needed for construction. This is crucial for efficient resource management and cost estimation in building projects.
The area of the base of an oblique pyramid with a square base is calculated using the formula B = h 3 V . This means the area is directly proportional to the volume and inversely proportional to the height. Therefore, the chosen option is D: h 3 V units 2 .
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