Answer :
Answer: [tex]11.15 in^{3}[/tex]
Explanation:
We need to know the volume of the cone that can be filled with bubble gum ball, but firstly we need to calculate the volume of the cone [tex]V_{C}[/tex] and the volume of the buble gum ball (a sphere) [tex]V_{B}[/tex]:
Volume of the cone:
[tex]V_{C}=\frac{\pi R^{2}h}{3}[/tex] (1)
Where:
[tex]R=1.75 in[/tex] is the radius of the cone
[tex]h=3.5 in[/tex] is the height of the cone
[tex]V_{C}=\frac{\pi (1.75 in)^{2}3.5 in}{3}[/tex] (2)
[tex]V_{C}=11.22 in^{3}[/tex] (3) This is the volume of the cone
Volume of the gum ball:
[tex]V_{B}=\frac{4\pi r^{3}}{3}[/tex] (4)
Where:
[tex]r=\frac{0.5 in}{2}=0.25 in[/tex] is the radius of the sphere (half the diameter)
[tex]V_{B}=\frac{4\pi (0.25 in)^{3}}{3}[/tex] (5)
[tex]V_{B}=0.065 in^{3}[/tex] (6) This is the volume of the gum ball
Know we are able to find the closest approximation of the volume of the cone that can be filled with bubble gum ball, by calculating the difference or substracting (6) from (3):
[tex]V_{C}-V_{B}=11.22 in^{3}-0.065 in^{3}[/tex] (7)
Finally:
[tex]V_{C}-V_{B}=11.15 in^{3}[/tex] (8)