To determine the shape formed when triangle ABC rotates about side CB, we need to analyze the triangle's dimensions.
Triangle ABC has the following vertices:
- A(0,0)
- B(3,5)
- C(0,5)
When we rotate this triangle about side CB (which is a vertical line along the y-axis from C to B), we need to identify the relevant measurements:
-
The height of the cone formed will be the distance from point A to line CB, which is simply the x-coordinate of point A (0,0). The height (h) of the cone is the distance from point C to point A, which is 5 units (since C is at (0,5) and A is at (0,0)).
-
The radius (r) of the cone will be the horizontal distance from line CB to point A. As point A is at (0,0), the distance from the y-axis (line CB) is the x-coordinate of point A, which is also 0 units. However:
To find the maximum radius of the base of the cone, we look at point B, which has coordinates (3,5). As point B is directly above point A by 5 units and horizontally 3 units away from the y-axis, the radius at the top of the cone won't affect the height of the formed solid.
In summary:
- The height of the cone is 5 units (from point C(0,5) to point A(0,0)).
- The radius corresponding to point B is 3 units.
Therefore, the cone formed by rotating triangle ABC about side CB has:
- Height = 5 units
- Diameter (which is twice the radius) = 2 * 3 = 6 units
Thus, the correct answer is: a cone with a diameter of 6 units and a height of 5 units.