Question

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:
$v = \frac{1}{3}a^2h$.
which equation correctly rewrites the formula to solve for h?
a. $h = \frac{3v^2}{a}$
b. $h = \frac{va^2}{3}$
c. $h = 3va^2$
d. $h = \frac{3v}{a^2}$

Explanation:

Step1: Start with the volume formula

We have the formula for the volume of a right square pyramid: \( V=\frac{1}{3}a^{2}h \).

Step2: Isolate \( h \)

To solve for \( h \), we first multiply both sides of the equation by \( 3 \) to get rid of the fraction. This gives us \( 3V = a^{2}h \).

Step3: Solve for \( h \)

Then, we divide both sides of the equation \( 3V = a^{2}h \) by \( a^{2} \) (assuming \( a
eq0 \)). So, \( h=\frac{3V}{a^{2}} \).

Answer:

D. \( h = \frac{3V}{a^2} \)