The section of a right circular cone by a plane through its vertex perpendicular to the base is an equilateral triangle each side of which is 12 m. Find the volume of the cone.

Explanation

To find the volume of the cone given that the section through its vertex perpendicular to the base is an equilateral triangle with each side measuring 12 m, we can follow these steps:

### Step 1: Understand the Geometry
The cross-section of the cone through the vertex is an equilateral triangle. Each side of the triangle is 12 m.

### Step 2: Determine the Height of the Triangle
In an equilateral triangle, the height (h) can be calculated using the formula:
\[
...