Answer:
A
Step-by-step explanation:
First, let's find the total volume of the cone by itself. The volume of a cone is givne by:
[tex]\displaystyle V = \frac{1}{3} \pi r^2h[/tex]
Since the radius of the cone is two inches and the height is three inches:
[tex]\displaystyle V_\text{cone} = \frac{1}{3}\pi (2^2)(3)[/tex]
Next, find the volume of the sphere of bubble gum. The volume of a sphere is given by:
[tex]\displaystyle V=\frac{4}{3} \pi r^3[/tex]
Since the diameter of the bubble gum is 0.5 inches, the radius is 0.25 inches.
Therefore, the volume of the bubble gum is:
[tex]\displaystyle V =\frac{4}{3} \pi (0.25^3)[/tex]
The amount of cone that will be filled with flavored ice will be the total volume of the cone minus the volume of the cone that will be filled with bubble gum. Therefore:
[tex]\displaystyle \frac{1}{3}\pi (2^2)(3) - \frac{4}{3}\pi (0.25^3)[/tex]
By letting π = 3.14:
[tex]\displaystyle \frac{1}{3}(3.14) (2^2)(3) - \frac{4}{3}(3.14) (0.25^3)[/tex]
Therefore, our answer is A.
