Question

Jon started with a diagram like the on below and drew a three-dimensional figure by rotating the circle 360 degrees about line m.

Nadia started with a diagram like the one shown below and drew a three-dimensional figure by rotating the right triangle ABC 360 degrees about line n.


(See photo provided.)


I need:

1. The three dimensional figure created by each person

I think that Jon made a Torus and Nadia made a Cone

2. The planes of symmetry of the three-dimensional figures created by each person. Nadia says her figure has an infinite number of planes of symmetry, and Jon says his figure has an infinite number plus one, and convinces Nadia. How might Jon have explained this?

The other explanations online for part 2 of this question are incorrect, or make no sense to me.

Answer 1

Jon's figure is a torus.

Nadia's figure is a cone.

Explanation:

A torus is a shape that resembles a doughnut. It is formed by revolving a circle in 3 D space about an axis co-planar with the circle.

It is also true that Jon’s figure has one more plane of symmetry than Nadia’s because his figure has one more plane around it, while Nadia’s figure has not.

Answer 2

1. correct
2. see below

Explanation:

2.

The cone has an axis of symmetry that is the line around which the original figure was rotated. Likewise for the torus. The infinite number of planes that exist at all the different angles of rotation relative to that axis are all planes of symmetry.

In addition, the torus has a plane of symmetry perpendicular to that axis and through the center of the circle.