Hello!
The answer is:
We will have to fill 226.194 cubic inches.
Why?
To solve the problem, we need to find the volume of the flower vase, and then, calculate the two third parts of its volume. Also, from the statement we know that the shape of the flower vase is a right cylinder, since the only given information about it, is its diameter and height.
We can calculate the volume of a right cylinder using the following equation:
[tex]V_{Cylinder}=\pi radius^{2}*height[/tex]
So, we are given the following information:
[tex]diameter=6in\\radius=\frac{diameter}{2}=\frac{6in}{2}=3in\\height=12in[/tex]
Then,
Substituting the given information, and calculating, we have:
[tex]V_{Cylinder}=\pi *(3in)^{2}*12in=108\pi=339.292in^{3}[/tex]
Now, calculating how many cubic inches are [tex]\frac{2}{3}[/tex] of the flower vase volume, we have:
[tex]VolumeToFill=CubicInchesToFill=\frac{2}{3}*Volume\\\\CubicInchesToFill=\frac{2}{3}*339.292in^{3} =226.194in^{3}[/tex]
Hence, we have that we will have to fill 226.194 cubic inches.
Have a nice day!
