A cylinder is intersected by a plane inclined at an angle of 60 degrees to its axis. What is the shape of the resulting cross-section?

The logic follows here is:

When a plane intersects a cylinder at an angle to its axis, the shape of the resulting cross-section depends on the angle of intersection. If the plane is perpendicular to the axis, the cross-section is a circle. If the plane is parallel to the axis, the cross-section is a rectangle. However, when the plane intersects the cylinder at any other angle, the resulting cross-section is an ellipse. In this specific case, the plane is inclined at an angle of 60 degrees to the axis of the cylinder. This means the plane is neither perpendicular nor parallel to the axis, but intersects it obliquely.

Therefore, the resulting cross-section will be an ellipse.

Hence, the correct answer is "Option 3".

1) Spiral → A spiral cannot be the cross-section of a cylinder by a plane.

2) Parabola → A parabola is formed when a plane intersects a cone, not a cylinder.

4) Hyperbola → A hyperbola is formed when a plane intersects a double cone at an angle.