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`

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)=(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)= (1)/(3)(99\ in^3)\\\\V_(cone)=33\ in^3`