Cross-sections & slicing drills

Determine the 2D cross-section produced by slicing a 3D solid.

Free, timed SHSAT practice sets on cross-sections & slicing— every question includes a full worked explanation, and there's no account required.

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How to solve cross-section problems

A cross-section is the flat face you see when you slice a solid with a straight cut. Picture the knife, then ask which way it cuts.

Common traps: answering with the shape of the side you see instead of the cut, and forgetting that a slice parallel to the base of a pyramid is smaller but still the same shape as the base.

Worked examples

Example 1.
A square pyramid is sliced by a plane parallel to its square base. What shape is the resulting cross-section?
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Answer:
C

A square pyramid is sliced by a plane parallel to its square base. The resulting cross-section is a square.

Example 2.
A cylindrical log is sliced by a plane perpendicular to its base, straight through the center. What shape is the resulting cross-section?
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Answer:
B

A cylindrical log is sliced by a plane perpendicular to its base, straight through the center. The resulting cross-section is a rectangle.

Example 3.
A plane slices through a cone. Which of the following is NOT a possible shape of the resulting cross-section?
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Answer:
B

Slicing a cone with a plane can produce a circle, triangle, or oval (ellipse), but never a square -- that shape is not achievable from any planar slice of a cone.