Select the correct answer.
This is the formula for the volume of a right square pyramid, where $a$ is the side length of the base and $h$ is the height:
[tex]$V=\frac{1}{3} a^2 h$[/tex]
Which equation correctly rewrites the formula to solve for $h$?
A. [tex]$h=\frac{3 V}{a^2}$[/tex]
B. [tex]$h=\frac{V a^2}{3}$[/tex]
C. [tex]$h=\frac{3 V^2}{a}$[/tex]
D. [tex]$h=3 V a^2$[/tex]
Answer (1)
Multiply both sides of the equation by 3: 3 V = a 2 h .
Divide both sides of the equation by a 2 : h = a 2 3 V .
The equation correctly rewritten to solve for h is h = a 2 3 V .
The correct answer is h = a 2 3 V .
Explanation
Understanding the Formula We are given the formula for the volume of a right square pyramid: V = 3 1 a 2 h , where a is the side length of the base and h is the height. Our goal is to isolate h on one side of the equation.
Multiplying by 3 To isolate h , we first multiply both sides of the equation by 3: 3 V = a 2 h
Dividing by a 2 Next, we divide both sides of the equation by a 2 :
a 2 3 V = h
The Solution Therefore, the equation correctly rewritten to solve for h is: h = a 2 3 V
Examples
Understanding how to rearrange formulas is crucial in many real-world applications. For example, if you are designing a square pyramid-shaped container with a specific volume and base side length, you can use the rearranged formula to determine the required height of the container. This principle extends to various fields, such as architecture, engineering, and even cooking, where adjusting ingredient quantities based on desired volume is essential.
