The shapes of the horizontal cross-sections of the cone below are not all congruent.A.TrueB.False

Analyzing the Question

The question revolves around the shapes of the horizontal cross-sections of a cone.

Understanding the Cone

1. Definition of a Cone: A cone is a three-dimensional geometric shape with a circular base that tapers smoothly from the base to a point called the apex.

2. Horizontal Cross-Sections: When a cone is sliced horizontally (parallel to the base), the resulting cross-section is a circle. The radius of this circle varies depending on the height at which the slice is made.

Evaluating Congruency

1. Top Cross-Section: The top cross-section (near the apex) will be a smaller circle.
2. Middle Cross-Section: As we move downwards toward the base, the radius increases until it reaches the same size as the base.
3. Bottom Cross-Section: The bottom cross-section (at the base) is the largest circle.

Conclusion

Since the horizontal cross-sections at different heights result in circles of varying radii, they are not all congruent.

Final Answer

B. False - The shapes of the horizontal cross-sections of the cone are not all congruent.