Using the method of integration, show that the volume of a right circular cone of base radius r and height h is `V=1/3pir^2h`.

Explanation

To find the volume of a right circular cone with base radius \( r \) and height \( h \) using integration, we can follow these steps:

### Step 1: Set Up the Cone
Consider a right circular cone with its vertex at the origin (0, 0) and the base at height \( h \). The radius of the base is \( r \). We will slice the cone into thin disks perpendicular to the height.

### Step 2: Define the Thickness and Radius of the Disk
Let \( x \) be the height from the vertex of the cone to the disk. The thickness of the disk is \( dx \). The radius of the disk at height \( x \) is denoted as \( y \).

...