Question

the cylinder and the sphere below have the same radius and the same volume. what is the height of the cylinder? v_{cylinder}=\pi r^{2}h v_{sphere}=\frac{4}{3}\pi r^{3} 9m 4m 6m 8m

Explanation:

Step1: Set volume equations equal

Since $V_{cylinder}=V_{sphere}$, we have $\pi r^{2}h=\frac{4}{3}\pi r^{3}$.

Step2: Cancel out common terms

Divide both sides of the equation by $\pi r^{2}$ (assuming $r
eq0$). We get $h = \frac{4}{3}r$.

Step3: Substitute the radius value

Given $r = 6m$, then $h=\frac{4}{3}\times6m$.
$h = 8m$.

Answer:

$8m$