Geometry
GradesGrade 7GeometryCross Sections of 3D Figures

Cross Sections of 3D Figures

📐 Geometry
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Cross Sections of 3D Figures

Slice a 3D solid and look at the flat shape you reveal — that is the cross section!

A CROSS SECTION is the 2D shape you see when you make a flat cut through a 3D solid. Different cuts of the same solid can reveal different shapes. Visualizing cross sections builds powerful spatial reasoning.

🧊Cross sections of a cube
Slice a cube:
• Horizontally (parallel to base) → square
• Diagonally (edge to edge) → rectangle
• Cutting through 6 faces diagonally → hexagon!

The same solid yields many different cross sections depending on angle.

Cross sections of a cone

Horizontal → circleAngled → ellipseThrough the apex vertically → triangle

Cross sections of a cylinder

Horizontal → circleVertical → rectangleAngled → ellipse

The angle and direction of the cut determines which 2D shape appears!

How to determine a cross section:

1Visualize the 3D solid clearly
2Decide the direction of the cut (horizontal, vertical, or diagonal)
3Trace which faces or surfaces the cutting plane intersects
4The boundary where the plane meets the solid forms the cross-section shape

Cross sections of a rectangular pyramid:

Horizontal (near base) → large rectangleHorizontal (near tip) → small rectangleVertical through apex → triangleDiagonal → trapezoid

Higher horizontal cuts give smaller rectangles because the pyramid narrows toward its apex.

✏️ Try It!

If you slice a sphere with a flat cut through its center, what shape is the cross section?

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Remember This!

Try it at home! Slice an orange or a bell pepper in different directions. The cross-sectional shapes change depending on whether you cut horizontally, vertically, or at an angle.

Take Quiz 📝 — 25 Questions