Question

9 caroline know the height and the required volume of a cone - shaped vase she determine the radius of the vase? v = \frac{1}{3}\pi r^{2}h (a) r = \sqrt{\frac{v}{3\pi h}} (b) r = \sqrt{\frac{3v}{\pi h}} (c) r = \frac{\sqrt{3v}}{\pi h} (d) r = \pm\sqrt{\frac{3v}{\pi h}}

Explanation:

Step1: Isolate $r^{2}$

Given $V = \frac{1}{3}\pi r^{2}h$, multiply both sides by 3 to get $3V=\pi r^{2}h$. Then divide both sides by $\pi h$: $r^{2}=\frac{3V}{\pi h}$.

Step2: Solve for $r$

Take the square - root of both sides. Since $r$ represents the radius (a non - negative quantity in this context), we have $r=\sqrt{\frac{3V}{\pi h}}$.

Answer:

B. $r = \sqrt{\frac{3V}{\pi h}}$