Question
Suppose △ABC with A(0,0) , B(3,5) , and C(0,5) is rotated about side CB¯¯¯¯¯¯¯¯ . Identify the three-dimensional object formed.(1 point) Responses a cone with a diameter of 6 units and a height of 5 units a cone with a diameter of 6 units and a height of 5 units a cone with a diameter of 5 units and a height of 3 units a cone with a diameter of 5 units and a height of 3 units a cone with a height of 3 units and a diameter of 10 units a cone with a height of 3 units and a diameter of 10 units a cone with a height of 5 units and a diameter 3 units
Answers
GPT-4o mini
To determine the three-dimensional object formed by rotating triangle ABC about side CB, we need to understand the dimensions of the triangle.
1. The coordinates of the points are:
- \( A(0,0) \)
- \( B(3,5) \)
- \( C(0,5) \)
2. Side CB (which is vertical) goes from point C at (0,5) to point B at (3,5).
3. The height of the triangle (the height from point A to line CB) is the vertical distance from point A to line CB, which is 5 units.
4. The radius of the base when the triangle is rotated around CB corresponds to the horizontal distance from point A to line CB, which is 3 units.
The resulting figure when triangle ABC is rotated about line CB is a right circular cone.
Now, to identify the specific dimensions:
- The height of the cone is the vertical distance from point C to point A, which is 5 units.
- The diameter of the base of the cone is represented by the diameter of the circle formed by the rotation of point A around line CB. Since the radius is 3 units, the diameter will be \( 3 \times 2 = 6 \) units.
Thus, the three-dimensional object formed is a **cone with a diameter of 6 units and a height of 5 units**.
**Final Answer:** a cone with a diameter of 6 units and a height of 5 units.
1. The coordinates of the points are:
- \( A(0,0) \)
- \( B(3,5) \)
- \( C(0,5) \)
2. Side CB (which is vertical) goes from point C at (0,5) to point B at (3,5).
3. The height of the triangle (the height from point A to line CB) is the vertical distance from point A to line CB, which is 5 units.
4. The radius of the base when the triangle is rotated around CB corresponds to the horizontal distance from point A to line CB, which is 3 units.
The resulting figure when triangle ABC is rotated about line CB is a right circular cone.
Now, to identify the specific dimensions:
- The height of the cone is the vertical distance from point C to point A, which is 5 units.
- The diameter of the base of the cone is represented by the diameter of the circle formed by the rotation of point A around line CB. Since the radius is 3 units, the diameter will be \( 3 \times 2 = 6 \) units.
Thus, the three-dimensional object formed is a **cone with a diameter of 6 units and a height of 5 units**.
**Final Answer:** a cone with a diameter of 6 units and a height of 5 units.