Answer: [tex]V_{cone}=33\ in^3[/tex]
Step-by-step explanation:
For this exercise it is necessary to to remember the shown below:
1. The volume of a cylinder can be calculated with the following formula:
[tex]V_{cylinder}=\pi r^2h[/tex]
Where "r" is the radius and "h" is the height of the cylinder.
2. The volume of a cone can be calculated with the following formula:
[tex]V_{cone}=\frac{1}{3}\pi r^2h[/tex]
Where "r" is the radius and "h" is the height of the cone.
In this case you know that the volume of the cylindrical container is:
[tex]V_{cylinder}= 99\ in^3[/tex]
Knowing that the cone-shaped hat fit perfectly into the cylindrical container, then you can identify that:
[tex]V_{cone}= \frac{1}{3}(99\ in^3)\\\\V_{cone}=33\ in^3[/tex]
