Geometry worksheet on cross sections of 3D shapes with multiple choice, open-ended, and written response questions.

Let’s go step by step through each question.

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Question 1: Which of the following represents the cross section parallel to the base of the below figure?

The figure is a cone (pointy top, circular base).
A cross section parallel to the base means you slice it horizontally — like cutting a loaf of bread sideways.
For a cone, that gives you a circle.

Looking at the options:
- Circle → ✔ correct
- Triangle → no, that’s vertical cut
- Square/rectangle → not for cone
- Other shapes → no

→ Answer: Circle

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Question 2: Which of the following represents the cross section perpendicular to the base of the below figure?

Figure is a triangular prism (like a Toblerone bar — triangle on ends, rectangles on sides).

Perpendicular to the base = slicing straight down from top to bottom, across the length.

If you slice perpendicular to the triangular base, you get a rectangle (because you’re cutting along the rectangular face).

Wait — let’s think again.

Actually, if the “base” is the triangle, then perpendicular to the base would mean slicing vertically through the prism, which could give a rectangle or another triangle depending on direction.

But in standard problems, when they say “perpendicular to the base” for a prism, and show a triangular prism, they usually mean slicing across the length — giving a rectangle.

Options include: circle, triangle, square, rectangle, etc.

→ Best answer: Rectangle

*(Note: If sliced perpendicular to the triangular face along its height, you might get a triangle — but typically “perpendicular to the base” implies slicing across the lateral faces. Given common test questions, rectangle is expected.)*

Wait — let me double-check with logic:

Triangular prism has two triangular bases and three rectangular faces.

If you slice perpendicular to the base, meaning your knife goes straight down through the prism, crossing from one rectangular side to the other — you get a rectangle.

Yes → Rectangle

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Question 3: Which of the following represents the cross section parallel to the base of the below figure?

Figure is a pyramid with a square base (square pyramid).

Parallel to the base = horizontal slice.

That gives a smaller square (same shape as base, just smaller).

Options: circle, triangle, square, rectangle, pentagon...

→ Answer: Square

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Question 4: Which of the following represents the cross section perpendicular to the base of the below figure?

Same square pyramid.

Perpendicular to the base = vertical slice, going from apex down through the center of the base.

That gives a triangle (isosceles triangle).

Because you’re cutting through the apex and the middle of opposite sides of the square base.

→ Answer: Triangle

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Question 5: Which geometric figure below would have a hexagonal cross-section parallel to the base of the figure?

We need a solid whose base is a hexagon, so that a horizontal slice gives a hexagon.

Look at the figures:

- First: looks like a hexagonal prism? Or maybe a cylinder? No — first figure is a green hexagonal prism? Wait, actually looking at typical diagrams:

Usually:

- A hexagonal prism has hexagons as bases → parallel cross section = hexagon ✔

Other options:

- Cone → circle
- Cylinder → circle
- Pyramid with triangular base → triangle
- Rectangular prism → rectangle

So only the hexagonal prism will give a hexagon when sliced parallel to base.

In the image, the fourth figure (purple) looks like a hexagonal prism.

→ Answer: Hexagonal prism (the purple one)

*(Assuming standard labeling — since we can’t see exact colors, but based on shape: the one with hexagon-shaped ends.)*

Actually, rechecking: the question says “which geometric figure below” — and lists 5 figures.

Typical setup:

1. Green: possibly a triangular prism?
2. Blue: cone?
3. Orange: rectangular prism?
4. Purple: hexagonal prism ← this one
5. Red: maybe a pyramid?

Yes → Figure 4 (purple hexagonal prism)

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Now Open Ended:

Question 6: Describe the cross section taken in the cylinder below. Is it parallel or perpendicular to the base?

Cylinder shown with a diagonal slice? Wait — description says: “the cross-section is perpendicular to the base and forms a rectangle.”

Actually, if you slice a cylinder perpendicular to the base (i.e., vertically), you get a rectangle.

If you slice parallel to the base → circle.

The problem says: “Describe the cross section... Is it parallel or perpendicular?”

And there’s a diagram — likely showing a vertical slice → rectangle.

Also, text says: “the cross-section is perpendicular to the base and forms a rectangle.”

So answer should confirm that.

→ The cross section is perpendicular to the base and forms a rectangle.

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Question 7: Describe the cross section taken in the cylinder below.

Diagram shows a diagonal slice? Text says: “The cross-section is diagonal to the base, forming an ellipse.”

Yes — if you slice a cylinder at an angle (not parallel, not perpendicular), you get an ellipse.

→ Answer: The cross section is diagonal to the base and forms an ellipse.

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Question 8: Sketch a 3-D geometric shape that would have a circular cross section parallel to the base, and a triangular cross-section perpendicular to the base.

What shape has:

- Circular cross section when sliced parallel to base → so base must be circle → cone or cylinder.
- Triangular cross section when sliced perpendicular to base → cylinder gives rectangle, cone gives triangle!

Yes — cone!

Slice cone horizontally → circle.

Slice cone vertically through apex → triangle.

Perfect.

→ Sketch a cone.

(You don’t need to draw here, but describe: It’s a cone.)

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Question 9: Sketch a 3-D geometric shape that would have a pentagonal and rectangular cross section.

Need a shape that can give both pentagon and rectangle as cross sections.

Best candidate: pentagonal prism.

Why?

- Slice parallel to base → pentagon.
- Slice perpendicular to base (along the length) → rectangle.

Yes.

Alternatively, a pentagonal pyramid could give pentagon (parallel) and triangle (perpendicular) — not rectangle.

So pentagonal prism is best.

→ Sketch a pentagonal prism.

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Written Response:

Question 10: Compare and contrast the cross sections of a cube and a triangular prism.

Cube:

- All faces are squares.
- Cross sections:
- Parallel to any face → square.
- Perpendicular to face → also square (if aligned).
- Diagonal cuts → can give rectangles, triangles, hexagons, etc.

Triangular Prism:

- Two triangular bases, three rectangular faces.
- Cross sections:
- Parallel to triangular base → triangle.
- Perpendicular to triangular base (along length) → rectangle.
- Other angles → trapezoids, parallelograms, etc.

Compare:

- Both can produce rectangles as cross sections.
- Cube always gives regular polygons (squares, equilateral triangles, regular hexagons) if cut symmetrically.
- Triangular prism gives triangles and rectangles naturally.

Contrast:

- Cube has all identical faces; triangular prism has different face types.
- Cube cannot give a triangle unless cut diagonally; triangular prism gives triangle easily when cut parallel to base.

Simple version for student:

> A cube can make squares, rectangles, triangles, or even hexagons depending on how you slice it. A triangular prism makes triangles when you slice it like the end, and rectangles when you slice it along the long way. Both can make rectangles, but only the triangular prism naturally makes triangles without tilting the knife.

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Question 11: Compare and contrast the cross sections of the two geometric figures below.

Figures: left is a cone, right is a square pyramid.

Cross sections:

Cone:

- Parallel to base → circle
- Perpendicular to base (through apex) → triangle
- Diagonal → ellipse

Square Pyramid:

- Parallel to base → square (smaller)
- Perpendicular to base (through apex) → triangle
- Diagonal → trapezoid or irregular quadrilateral

Compare:

- Both can give triangles when sliced vertically through the apex.
- Both taper to a point.

Contrast:

- Cone gives circles and ellipses; pyramid gives squares and trapezoids.
- Cone’s parallel slices are curved (circles); pyramid’s are flat polygons (squares).
- Pyramid has flat faces; cone has one curved surface.

Student-friendly:

> Both the cone and the square pyramid can be sliced to make triangles if you cut straight down from the tip. But if you slice them sideways, the cone makes circles (like coins), while the pyramid makes smaller squares. Also, the cone’s side is smooth and curved, so diagonal slices make ovals (ellipses), but the pyramid’s sides are flat, so diagonal slices make four-sided shapes like trapezoids.

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Final Answers compiled:

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Final Answer:

1. Circle
2. Rectangle
3. Square
4. Triangle
5. Hexagonal prism (purple figure)
6. The cross section is perpendicular to the base and forms a rectangle.
7. The cross section is diagonal to the base and forms an ellipse.
8. Cone
9. Pentagonal prism
10. A cube can create squares, rectangles, triangles, or hexagons when sliced. A triangular prism creates triangles when sliced parallel to its base and rectangles when sliced perpendicular to its base. Both can form rectangles, but only the triangular prism naturally forms triangles without angled cuts.
11. Both the cone and square pyramid can form triangles when sliced vertically through the apex. However, slicing parallel to the base gives a circle for the cone and a square for the pyramid. The cone’s curved surface allows elliptical cross sections when sliced diagonally, while the pyramid’s flat faces result in trapezoidal or quadrilateral cross sections.