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]$h=\frac{3 V^2}{6}$[/tex]
C. [tex]$h=3 V a^2$[/tex]
D. [tex]$h=\frac{V a^2}{3}$[/tex]
Answer (2)
Isolate h in the equation V = 3 1 a 2 h :
Multiply both sides by 3: 3 V = a 2 h .
Divide both sides by a 2 : h = a 2 3 V .
The correct equation is h = a 2 3 V .
Explanation
State the given formula and objective. 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. We want to solve for h .
Multiply both sides by 3. To isolate h , we first multiply both sides of the equation by 3:
3 V = a 2 h
Divide both sides by a 2 .
Next, we divide both sides of the equation by a 2 :
h = a 2 3 V
State the final answer. Therefore, the equation correctly rewritten to solve for h is:
h = a 2 3 V
This corresponds to option A.
Examples
Understanding how to rearrange formulas is crucial in many real-world applications. For instance, if you're designing a square-based pyramid-shaped container and you know the desired volume and base side length, you can use the rearranged formula to determine the necessary height. This ensures your container meets the required specifications, whether it's for packaging, architecture, or even creating a unique piece of art. The ability to manipulate formulas allows for precise control over design parameters, saving time and resources in the process.
To solve for the height h of a right square pyramid from its volume formula V = 3 1 a 2 h , we multiply both sides by 3 and divide by a 2 , leading to h = a 2 3 V . Therefore, the correct answer is option A.
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