Question

the formula for finding the volume $v$ of a right cone is $v = \frac{1}{3}\pi r^{2}h$, where $r$ represents the radius of the circular base and $h$ represents the height of the cone. which equation expresses the height of a right cone in terms of its volume and radius?
a $h = \frac{3v}{\pi r^{2}}$
b $h = \frac{v}{3\pi r^{2}}$
c $h = \frac{3v}{\pi r}$
d $h = \frac{v}{3\pi r}$

Explanation:

Step1: Start with the volume formula

$$V = \frac{1}{3}\pi r^2 h$$

Step2: Isolate $\pi r^2 h$

Multiply both sides by 3:
$$3V = \pi r^2 h$$

Step3: Solve for $h$

Divide both sides by $\pi r^2$:
$$h = \frac{3V}{\pi r^2}$$

Answer:

A. $h = \frac{3V}{\pi r^2}$