The volume of a cone is found by multiplying the area of the circular base by the height of the cone, and then dividing the product by 3. The area of the base is found by taking the square of the radius and multiplying it by pi.
The height of the cone is different from the slant height. The slant height is the length of a straight line segment running from the vertex of the cone to the perimeter of the base. The height of the cone is the length of a line segment drawn perpendicular to the base connecting the base to the vertex. In the case of a right circular cone, that perpendicular line intersects the base at the center of the circle.