Answer:
[tex]72\pi\ in^{3}[/tex]
Step-by-step explanation:
step 1
Calculate the volume of the cylinder (flower vase)
The volume is equal to
[tex]V=\pi r^{2}h[/tex]
we have
[tex]r=6/2=3\ in[/tex] -----> the radius is half the diameter
[tex]h=12\ in[/tex]
substitute the values
[tex]V=\pi (3)^{2}(12)=108\pi\ in^{3}[/tex] ------> exact value
step 2
Calculate 2/3 of the volume
[tex]V=(2/3)108\pi=72\pi\ in^{3}[/tex]
