Respuesta :
You can use the fact that ice filling will be done only in the space which is remaining in the cone that is left after filling one bubble gum inside the cone.
The volume of the cone that can be filled with flavored ice is given by:
Option B: [tex]\dfrac{1}{3}\pi (4)^26 - \dfrac{4}{3}\pi (0.4)^3[/tex]
How to calculate remaining volume of cone?
The remaining volume of cone will be calculated as volume of cone - volume that that spherical ball takes up. Volume shows space. If given cone has some space and bubble gum ball comes in, it takes some space and thus rest of the space will be available for ice filling. This can be calculated by subtracting total volume of cone with total volume that bubble gum ball has.
What is the volume of empty cone and of that spherical bubble gum ball?
We can use the formula for finding the volume of cone and the volume of sphere.
The formula goes like this:
Volume of right circular cone with radius r and height h = [tex]\dfrac{1}{3}\pi r^2h[/tex]
Thus, volume of snow cone = [tex]\dfrac{1}{3} \times \pi \times (4)^2 \times (6)[/tex] cubic inches.
Volume of sphere with radius r is given by [tex]\dfrac{4}{3}\pi r^3[/tex]
Since the bubble gum ball has diameter 0.8, thus radius is half of it which is 0.8/2 = 0.4.
The volume of bubble gum ball is [tex]\dfrac{4}{3} \pi (0.4)^3[/tex] cubic inches.
Thus, the remaining volume(space) for filling flavored ice is calculated by
Remaining volume for ice filling = Total cone volume - volume of ice filling
Remaining volume = [tex]\dfrac{1}{3}\pi (4)^26 - \dfrac{4}{3}\pi (0.4)^3[/tex] cubic inches.
Thus, the volume of cone that can be filled with flavored ice is given by:
[tex]\dfrac{1}{3}\pi (4)^26 - \dfrac{4}{3}\pi (0.4)^3[/tex]
Learn more about volume of cone and volume of sphere here:
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