Question

A frustum is formed when a plane that is parallel to a cone’s base cuts off the upper portion, as shown below.

Answer 1

Answer:

44 pi

Step-by-step explanation:

Answer 2

Answer: $44\pi \ \ units^3$

Step-by-step explanation:

The formula for calculate the volume of a cone is:

$V=\frac{1}{3}\pi r^2h$

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:

$r=4\ units\\h=6\ units+3\ units=9\ units$

Therefore, substituting into the formula, you get:

$V_{total}=\frac{1}{3}\pi (4\ units)^2(9\ units)=48\pi \ \ units^3$

Let's calculate the volume of the upper portion. You can identify that:

$r=2\ units\\h=3\ units$

Therefore, this is:

$V_{1}=\frac{1}{3}\pi (2\ units)^2(3\ units)=4\pi \ \ units^3$

Then, the volume of the frustum is:

$V_2=V_{total}-V_1\\\\V_2=48\pi \ \ units^3-4\pi \ \ units^3\\\\V_2=44\pi \ \ units^3$