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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].

Sagot :

Certainly! Let's solve the formula \( V = \frac{1}{5} s^2 h \) for \( s \).

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

2. Isolate \( s^2 \) on one side of the equation:
To eliminate the fraction, multiply both sides by 5:
[tex]\[ 5V = s^2 h \][/tex]

3. Solve for \( s^2 \):
Divide both sides of the equation by \( h \) to solve for \( s^2 \):
[tex]\[ s^2 = \frac{5V}{h} \][/tex]

4. Take the square root of both sides to solve for \( s \):
[tex]\[ s = \sqrt{\frac{5V}{h}} \][/tex]

Now that we have the formula for \( s \), let's substitute hypothetical values for \( V \) and \( h \) to find \( s \). Assume the volume \( V \) of each piece is 100 cubic units and the height \( h \) is 10 units.

5. Substitute \( V = 100 \) and \( h = 10 \) into the equation:
[tex]\[ s = \sqrt{\frac{5 \times 100}{10}} \][/tex]

6. Simplify the expression inside the square root:
[tex]\[ s = \sqrt{\frac{500}{10}} \][/tex]

7. Further simplify the division:
[tex]\[ s = \sqrt{50} \][/tex]

Thus, the value of \( s \) is approximately:
[tex]\[ s = \sqrt{50} \approx 7.0710678118654755 \][/tex]

Hence, the value of [tex]\( s \)[/tex] when [tex]\( V = 100 \)[/tex] and [tex]\( h = 10 \)[/tex] is approximately 7.0710678118654755 units.