The volume of a cone can be found as:
[tex]V=\frac{1}{3}\pi r^2 h \\ \\ \\ Where: \\ \\ V:Volume \\ \\ r:radius \ of \ base \\ \\ h:height[/tex]
Given the radius and height, we can find the volume of the cone:
[tex]V=\frac{1}{3}\pi r^2 h \\ \\ V=\frac{1}{3}\pi (1.25)^2(2.75) \\ \\ V=\frac{1}{3}\pi(1.5625)(2.75) \\ \\ V\approx 4.5in^3[/tex]
The volume of a sphere is:
[tex]V=\frac{4}{3}\pi r^3 \\ \\ \text{Each gum ball has a diameter of 0.5in, so the radius is:} \\ \\ r=\frac{0.5}{2}=0.25in[/tex]
So, for each gum ball the volume is:
[tex]V=\frac{4}{3}\pi r^3 \\ \\ V=\frac{4}{3}\pi (0.25)^3 \\ \\ V=0.065in^3[/tex]
Therefore, the he closest approximation of the volume of the cone that can be filled with flavored ice is:
[tex]4.5-0.065=4.43in^3[/tex]
Conclusion: The volume of the cone that can be filled with flavored ice is 4.43 cubic inches.
