Math  /  Geometry

QuestionWhich figure has the same horizontal and vertical cross-sections? A C B D

Studdy Solution

STEP 1

Assumptions
1. We are given four geometric figures: A (square pyramid), B (trapezoidal prism), C (sphere), and D (cone).
2. We need to determine which figure has the same horizontal and vertical cross-sections.
3. Horizontal cross-sections are parallel to the base of the figure.
4. Vertical cross-sections are perpendicular to the base of the figure.

STEP 2

Analyze Figure A (Square Pyramid)
1. A square pyramid has a square base and triangular sides.
2. Horizontal cross-sections of a square pyramid are squares that decrease in size as they move up from the base.
3. Vertical cross-sections of a square pyramid are triangles.

Conclusion: The horizontal and vertical cross-sections are not the same.

STEP 3

Analyze Figure B (Trapezoidal Prism)
1. A trapezoidal prism has trapezoidal bases and rectangular sides.
2. Horizontal cross-sections of a trapezoidal prism are trapezoids.
3. Vertical cross-sections of a trapezoidal prism are rectangles.

Conclusion: The horizontal and vertical cross-sections are not the same.

STEP 4

Analyze Figure C (Sphere)
1. A sphere is a perfectly symmetrical 3D shape.
2. Horizontal cross-sections of a sphere are circles.
3. Vertical cross-sections of a sphere are also circles.

Conclusion: The horizontal and vertical cross-sections are the same.

STEP 5

Analyze Figure D (Cone)
1. A cone has a circular base and a pointed top.
2. Horizontal cross-sections of a cone are circles that decrease in size as they move up from the base.
3. Vertical cross-sections of a cone are triangles.

Conclusion: The horizontal and vertical cross-sections are not the same.

STEP 6

Based on the analysis, Figure C (Sphere) has the same horizontal and vertical cross-sections, which are circles.
The figure with the same horizontal and vertical cross-sections is Figure C (Sphere).

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