Answer: [tex]44\pi \ \ units^3[/tex]
Step-by-step explanation:
The formula for calculate the volume of a cone is:
[tex]V=\frac{1}{3}\pi r^2h[/tex]
Where "r" is the radius and "h" is the height.
Let's calculate the volume of the entire cone before the plane cut off the upper portion. You can identify that:
[tex]r=4\ units\\h=6\ units+3\ units=9\ units[/tex]
Therefore, substituting into the formula, you get:
[tex]V_{total}=\frac{1}{3}\pi (4\ units)^2(9\ units)=48\pi \ \ units^3[/tex]
Let's calculate the volume of the upper portion. You can identify that:
[tex]r=2\ units\\h=3\ units[/tex]
Therefore, this is:
[tex]V_{1}=\frac{1}{3}\pi (2\ units)^2(3\ units)=4\pi \ \ units^3[/tex]
Then, the volume of the frustum is:
[tex]V_2=V_{total}-V_1\\\\V_2=48\pi \ \ units^3-4\pi \ \ units^3\\\\V_2=44\pi \ \ units^3[/tex]
