The oblique circular cone has an altitude and a diameter of base that are each of length 12 cm. The line segment joining the vertex to the center of the base is the axis of the cone.

Question

The oblique circular cone has an altitude and a diameter of base that are each of length 12 cm. The line segment joining the vertex to the center of the base is the axis of the cone.

12 cm

12 cm

An oblique circular cone has a horizontal base. There are two dashed line segments, a labeled angle, and two labeled distances.

1. The diameter of the base is labeled 12 cm.
2. The altitude is labeled 12 cm.
3. The first dashed line segment extends down and to the left from the vertex of the cone to the center of its base.
4. The second dashed line segment extends horizontally from the left edge to the right edge of the base.
5. A right angle is formed with the second dashed line segment and the right vertical edge of the cone.

What is the length (in centimeters) of the axis?

Answer 1

You can use the Pythagorean theorem to solve for the "hypotenuse" of the triangle shown in your picture above. The base leg is 1/2 the diameter of the circle, so 6 (a), the side length is 12 (b). Pop that in and solve for c and that will be the length of the axis.