Subjects geometry

Cross Section Shapes

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1. **Problem Statement:** Identify the shape of the cross section formed when a plane slices through each given solid. 2. **Figure (a): Pentagonal Prism sliced vertically** - A pentagonal prism has a pentagon as its base. - A vertical slice parallel to the base will produce a cross section congruent to the base shape. - Therefore, the cross section is a pentagon, which corresponds to the shape □ (square) or a polygon with 5 sides. - Among the options, □ represents a square, but since the prism base is pentagonal, the cross section is a pentagon, which is not explicitly listed, but □ is the closest polygonal shape. 3. **Figure (b): Cone sliced horizontally** - A horizontal slice through a cone produces a circle. - This is because the cross section parallel to the base of a cone is always a circle. - Therefore, the cross section is ○ (circle). 4. **Figure (c): Pyramid sliced at an angle** - A pyramid sliced at an angle (not parallel to the base) produces a polygon with fewer sides than the base. - The cross section can be a triangle (△) or other polygons depending on the angle. - Given the options, △ (triangle) is the most likely cross section shape. **Final answers:** - (a) □ (pentagonal prism vertical slice approximated as polygon) - (b) ○ (circle) - (c) △ (triangle)