Subjects geometry

Vertical Plane Cross Section C8135A

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1. **Problem Statement:** Draw the cross section formed by a vertical plane that divides the solid into two congruent parts. 2. **Understanding the Solid:** The solid described is a cone on top of a cylinder. A vertical plane passing through the center axis divides the solid into two congruent halves. 3. **Cross-Section Shape:** - The vertical plane cuts through the cone, producing a triangular cross-section. - The same plane cuts through the cylinder, producing a rectangular cross-section. 4. **Is there more than one way to use a vertical plane to divide the figure into two congruent parts?** - Yes, any vertical plane passing through the central axis of the solid will divide it into two congruent parts. 5. **Does the cross-section change?** - No, because all such vertical planes through the axis produce the same cross-section shape: a triangle on top (from the cone) and a rectangle below (from the cylinder). 6. **Summary:** - The cross-section is a composite shape: a triangle (cone) above a rectangle (cylinder). - Different vertical planes through the axis yield congruent cross-sections.
Vertical Plane Rectangle (Cylinder) Triangle (Cone)