Question

type the correct answer in the box.
the formula for the volume, v, of a cone having the radius, r, and the height, h, is shown below.
$v = \frac{1}{3}\pi r^2 h$
write the formula to calculate the height, h.
$h = $

Explanation:

Step1: Start with the volume formula

We have the formula for the volume of a cone: \( V=\frac{1}{3}\pi r^{2}h \).

Step2: Isolate \( h \)

To solve for \( h \), we first multiply both sides of the equation by \( 3 \) to get rid of the fraction on the right - hand side. This gives us \( 3V=\pi r^{2}h \).
Then, we divide both sides of the equation by \( \pi r^{2} \) (assuming \( \pi r^{2}
eq0 \), which is valid for a cone with non - zero radius) to isolate \( h \). So, \( h = \frac{3V}{\pi r^{2}} \).

Answer:

\( h = \frac{3V}{\pi r^2} \)