Question

supposed triangleABC with
A (0,0)
B (3,5)
C (0,5)
is rotated aboutr side CB. identify the three-dimensional object formed

Answer 1

To understand the three-dimensional object formed when triangle ABC is rotated about side CB, we first need to define the setup clearly.

### Points of Triangle ABC:
- \( A(0, 0) \)
- \( B(3, 5) \)
- \( C(0, 5) \)

### Side CB:
Side CB runs vertically along the line from point C to point B, which is at the coordinates:
- B(3, 5), C(0, 5)

### Rotation:
When triangle ABC is rotated about side CB (which lies along the line \( x = 0 \) from y = 5 to y = 0), we are essentially spinning the triangle around this line, which gives us a three-dimensional object.

### Cross-Section:
As the triangle rotates around line CB:
- The vertex A (0, 0) rotates around the vertical line, creating a circular path.

- As point A moves, it traces out a circle with:
- Radius equal to the horizontal distance from point A to line CB, which is 0 units.
- Therefore, at point A, it does not create a circular path around line CB.

The true circular path comes from point B (3, 5), which is rotated around line CB (the vertical line at x = 0). This point B will create a circular path with a radius of 3 units (the horizontal distance from B to line CB).

### Formed Object:
Thus, the three-dimensional object generated by the rotation of triangle ABC about side CB is a **circular cone**:
- The base of the cone is a circle with radius 3 (the distance from line CB to point B).
- The height of the cone is the length along line CB from C(0, 5) down to A(0, 0), which is 5 units.

### Conclusion:
The resulting three-dimensional object from the rotation of triangle ABC about side CB is a **circular cone** with:
- Height = 5 units
- Base radius = 3 units.