To understand why the solid formed by rotating a right-angled triangle about any of its altitudes is a cone, let's break down the process step by step.


First, let's visualize a right-angled triangle. This triangle has one right angle (90 degrees) and two other angles, which are acute angles (less than 90 degrees). The side opposite the right angle is called the hypotenuse, and the other two sides are called the legs.


Now, let's consider one of the altitudes of the right-angled triangle. An altitude is a line segment drawn from one vertex of a triangle perpendicular to the opposite side. In this case, we can choose any of the three sides of the triangle to be the base, and the altitude will be the line segment perpendicular to that base.


Next, we rotate the right-angled triangle about its altitude. This means that we rotate the triangle in a circular motion, using the altitude as the axis of rotation. As the triangle rotates, it sweeps out a three-dimensional shape.


The resulting shape formed by rotating the right-angled triangle about its altitude is a cone. A cone is a three-dimensional geometric shape with a circular base and a pointed top called the apex. The altitude of the right-angled triangle becomes the axis of the cone, and the base of the cone is a circle that is parallel to the base of the triangle.


In conclusion, when a right-angled triangle is rotated about any of its altitudes, the resulting solid is a cone. This is because the rotation sweeps out a shape with a circular base and a pointed top, which matches the definition of a cone. Therefore, the correct answer to the question is option 'C' - Cone (Right Circular).