Question

Suppose
AABC with
A(0,0),
B(3,5), and
C(0, 5) is rotated about side CB. Identify the three-dimensional object formed. (1 point)
O 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
O a cone with a height of 5 units and
a diameter 3 units
a cone with a height of 3 units and a diameter of 10 units

Answer 1

To determine the three-dimensional object formed by rotating triangle AABC about side CB, we first need to understand the geometry of the triangle.

The coordinates of the points are:
- A(0,0)
- B(3,5)
- C(0,5)

When we visualize triangle AABC, we see that:
- Side CB is vertical, running from C(0,5) to B(3,5).
- The height of the triangle is determined by the vertical distance from point A(0,0) to line CB, which is a height of 5 units.

When triangle AABC is rotated about side CB, it will create a cone:
- The height of the cone corresponds to the vertical distance of point A from line CB, which is 3 units (the x-coordinate of point B).
- The diameter of the cone will be the distance across at the base when the triangle rotates, which corresponds to the distance from C to A, which equals 5 units (the y-coordinate of point B).

Thus, the resulting three-dimensional object is a cone that has:
- A height of 3 units (the horizontal distance from A to the line of rotation).
- A diameter of 5 units (determined by the height of point B).

So the correct answer is:
- **a cone with a height of 3 units and a diameter of 10 units.**

(Note: The correct interpretation considering the triangle's orientation would actually lead to it being a cone with a radius of 3 units, height of 5 units, leading to diameter being 6 units which is more accurately described as follows: A cone with a diameter of 6 units and a height of 5 units should be the corrected answer based on these measures).