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This is the formula for the volume of a right square pyramid, where [tex]a[/tex] is the side length of the base and [tex]h[/tex] is the height:
[tex]V=\frac{1}{3} a^2 h[/tex]

Which equation correctly rewrites the formula to solve for [tex]h[/tex]?

A. [tex]h=\frac{3 V^2}{a}[/tex]

B. [tex]h=\frac{V a^2}{3}[/tex]

C. [tex]h=\frac{3 V}{a^2}[/tex]

D. [tex]h=3 V a^2[/tex]

Sagot :

GinnyAnswer
To solve for [tex]\( h \)[/tex] in the volume formula of a right square pyramid [tex]\( V = \frac{1}{3} a^2 h \)[/tex], let's go through the steps carefully.

1. The given equation is:
[tex]\[ V = \frac{1}{3} a^2 h \][/tex]

2. To isolate [tex]\( h \)[/tex], we first need to eliminate the fraction. Multiply both sides of the equation by 3:
[tex]\[ 3V = a^2 h \][/tex]

3. Next, divide both sides of the equation by [tex]\( a^2 \)[/tex] to solve for [tex]\( h \)[/tex]:
[tex]\[ h = \frac{3V}{a^2} \][/tex]

Thus, the correct equation that rewrites the formula to solve for [tex]\( h \)[/tex] is:
[tex]\[ h = \frac{3V}{a^2} \][/tex]

Therefore, the correct choice is:
C. [tex]\( h = \frac{3V}{a^2} \)[/tex]
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