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]$\frac{3 V}{h}$[/tex] units [tex]$^2$[/tex]
B. [tex]$(3 V-h)$[/tex] units [tex]$^2$[/tex]
C. [tex]$(V-3 h)$[/tex] units [tex]$^2$[/tex]
D. [tex]$\frac{v}{3 h}$[/tex] units [tex]$^2$[/tex]
Answer (1)
The volume of a pyramid is given by V = 3 1 A h .
Solve the volume formula for the area of the base A .
Multiply both sides of the equation by 3: 3 V = A h .
Divide both sides by h : A = h 3 V .
The area of the base is h 3 V .
Explanation
Problem Analysis Let's analyze the problem. We are given the volume V and the height h of an oblique pyramid with a square base. We need to find an expression for the area of the base.
Volume Formula The formula for the volume of a pyramid is given by: V = 3 1 A h where V is the volume, A is the area of the base, and h is the height.
Solving for Area We need to solve for A , the area of the base. Multiplying both sides of the equation by 3, we get: 3 V = A h Now, divide both sides by h to isolate A :
A = h 3 V
Final Answer Therefore, the area of the base of the pyramid is h 3 V units 2 .
Examples
Imagine you're designing a modern art piece: an oblique pyramid with a square base. Knowing the volume and desired height, you can use the formula we derived to calculate the precise area of the base needed. This ensures your sculpture not only looks stunning but also adheres to your design specifications, blending artistic vision with mathematical precision.
