Question

A Party hat arrived in a cylindrical container in which it fit perfectly. If the volume of the container is 99in3. What is the volume of the cone-shaped hat?

Answer 1

Answer: $V_{cone}=33\ in^3$

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:

$V_{cylinder}=\pi r^2h$

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:

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

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:

$V_{cylinder}= 99\ in^3$

Knowing that the cone-shaped hat fit perfectly into the cylindrical container, then you can identify that:

$V_{cone}= \frac{1}{3}(99\ in^3)\\\\V_{cone}=33\ in^3$