A solid right square prism is cut into 5 equal pieces parallel to its bases. The volume of each piece is [tex]$V=\frac{1}{5} s^2 h$[/tex]. Solve the formula for [tex]$s$[/tex].

A. [tex]$s=\sqrt{\frac{5V}{h}}$[/tex]

B. [tex][tex]$s=\sqrt{\frac{h}{5V}}$[/tex][/tex]

C. [tex]$s=\sqrt{5Vh}$[/tex]

D. [tex]$s=\sqrt{5V-h}$[/tex]



Answer :

To solve for [tex]\( s \)[/tex] from the given formula [tex]\( V = \frac{1}{5} s^2 h \)[/tex], follow these steps:

1. Start with the given formula:
[tex]\[ V = \frac{1}{5} s^2 h \][/tex]

2. Isolate [tex]\( s^2 \)[/tex] by multiplying both sides of the equation by 5:
[tex]\[ 5V = s^2 h \][/tex]

3. Next, isolate [tex]\( s^2 \)[/tex] by dividing both sides of the equation by [tex]\( h \)[/tex]:
[tex]\[ s^2 = \frac{5V}{h} \][/tex]

4. Finally, solve for [tex]\( s \)[/tex] by taking the square root of both sides:
[tex]\[ s = \pm \sqrt{\frac{5V}{h}} \][/tex]

Since the problem is asking for the possible values of [tex]\( s \)[/tex], and geometric lengths are typically positive, we usually take the positive root in such contexts.

Therefore, the correct answer is:
[tex]\[ s = \sqrt{\frac{5V}{h}} \][/tex]

So the correct choice from the provided options is:

A. [tex]\(\sqrt{\frac{5V}{h}}\)[/tex]