The radius of the cylindrical vase is given to be 4 inches. Let us call it [tex] r [/tex]. Thus, [tex] r=4 [/tex]
Likewise, the height of the cylinder is given to be 10 inches. Thus, [tex] h=10 [/tex].
Now, we know that the volume of any cylinder is given by:
[tex] Volume=\pi r^{2}h [/tex]
Mary has been told that the vase should be filled 3/4.
Thus, 3/4th of the volume of the cylindrical vase will be:
[tex] Volume_{\frac{3}{4}} =\frac{3}{4}\pi r^2 h [/tex]
which in our case will become:
[tex] Volume_{\frac{3}{4}} =\frac{3}{4}\pi (4)^2 \times 10\approx377 [/tex]
Thus, the required volume of water to be filled is 377 [tex] in^3 [/tex]
