To visualize the three-dimensional object formed when triangle ABC is rotated about side CB, let's analyze the given points:
- A(0, 0)
- B(3, 5)
- C(0, 5)
First, we identify that side CB runs vertically along the y-axis from point C(0, 5) to point B(3, 5), which means it is a vertical line segment.
When we rotate triangle ABC about side CB (which is the line segment between points C and B), we will generate a three-dimensional shape. The rotation will sweep the area of the triangle outwards and create a solid.
To visualize the rotation:
- Point A(0, 0) will trace out a circle as it moves around line CB. The radius of this circle is the horizontal distance from point A to line CB, which is 3 units (the x-coordinate of point B).
- Points B(3, 5) and C(0, 5) lie along the y-axis and will not produce additional volume, as they are along the axis of rotation.
The shape generated by the rotation of triangle ABC around side CB is a circular cone. The height of the cone is the vertical distance between points C(0, 5) and the line through A(0, 0) (which is y=0), hence the height is 5 units. The radius of the cone is determined by the distance from A to the vertical line through CB (which is 3 units).
In summary, when triangle ABC is rotated about side CB, it forms a circular cone with:
- Height = 5 units
- Radius = 3 units