Answer: 11 in.
Step-by-step explanation:
Given
The volume of the cylindrical vase is [tex]216\ in^3[/tex]
Inside diameter is [tex]d=5\ in.[/tex]
[tex](\text{radius is given by }r=\dfrac{d}{2})[/tex]
Suppose, h is the height of the vase
Volume is given by
[tex]V=\pi r^2h[/tex]
Insert the values
[tex]\Rightarrow 216=\pi \times 2.5^2\times h\\\\\Rightarrow h=\dfrac{216}{6.25\times 3.142}\\\\\Rightarrow h=10.999\approx 11\ in.[/tex]
Thus, the height of the vase is [tex]11\ in.[/tex]
