Answer:
12.81 cubic inches
Explanation:
You want the volume of a cone with diameter 3.4 inches and slant height 4.56 inches.
Height
The height of the cone can be found using the Pythagorean theorem. It is the missing leg of a right triangle with hypotenuse 4.56 and leg (3.4/2) = 1.7.
h² + 1.7² = 4.56²
h = √(4.56² -1.7²) ≈ 4.2313 . . . . inches
Volume
The volume of the cone is give by the formula ...
V = 1/3πr²h
where r is the radius and h is the height.
Using r = 1.7 in and h ≈ 4.2313 in, we find the volume to be ...
V = (1/3)π·(1.7 in)²·(4.2313 in) ≈ 12.81 in³
The cone will hold about 12.81 cubic inches of water.
__
Additional comment
That's about 7.1 fluid ounces.