The shapes of the horizontal cross-sections of the cone below are all congruent.A.TrueB.FalseSUBMITarrow_backPREVIOUS

Break Down the Problem

1. Identify the Shape: The problem involves a cone and its horizontal cross-sections.
2. Understand Congruency: Congruent shapes are identical in shape and size.

Relevant Concepts

1. Horizontal Cross-Sections of a Cone: When a cone is sliced horizontally, the shape of the cross-section forms a circle. The radius of this circle changes as you move up or down the cone.
2. Congruence Definition: Two shapes are congruent if they can be made to coincide by rotations and translations.

Analysis and Detail

1. Examine Horizontal Cross-Sections:
   • At the base of the cone, the cross-section is a circle with maximum radius.
   • As you move upward, the radius of the horizontal cross-section decreases.
   • Therefore, the sizes of the cross-sections change based on the height of the slice.

Verify and Summarize

1. Conclusion on Congruency: Since the radius of the horizontal cross-sections varies as you move up the cone, the shapes are not all the same size or shape.

Final Answer

B. False - The horizontal cross-sections of a cone are not all congruent, as they vary in size.