# A conical tank with a radius of 4 ft and a height of 12 ft is filled with liquid. How much liquid has poured from the tip of the cone if the water level is 9 ft from the tip?

##### 3 Answers

See below

#### Explanation:

Volume of a cone:

We will use

This is the amount of water in the cone initially

Now when the water goes down to 9ft of height, the volume of water in the cone is:

This is the volume of water in the cone after water has been poured out.

So the amount of water poured out:

The original cone has height 12 feet and radius 4 feet. If 9 feet of height is lost by being poured out we need to find the volume of the smaller cone and subtract it from the larger one.

Using similar shapes to find the radius of the smaller cone.

Volume of a cone is

Volume of liquid remaining is

Another way to do it is to just find the volume of the frustum

#### Explanation:

The large cone has height 12 feet and radius 4 feet, the smaller cone has height 9 feet and radius 3 feet ( by using similar shapes)

Volume of a frustum is

Where