Three-Dimensional Figures Quiz - CBSE Class 9 Mathematics
Free practice quiz: Three-Dimensional Figures (CBSE Class 9 Mathematics). 17 multiple-choice questions with answers and explanations. Play online, no sign-up needed.
This CBSE Class 9 Mathematics practice quiz has 17 multiple-choice questions on Three-Dimensional Figures, and 17 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.
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Three-Dimensional Figures and Polyhedra
- A 3D figure (solid) has length, breadth and height, so it occupies space and has volume.
- A polyhedron is a solid whose faces are all flat polygons, like cubes, cuboids, prisms and pyramids.
- Cylinders, cones and spheres have curved surfaces, so they are not polyhedra.
Common mistake: Calling a cylinder or cone a polyhedron. Any solid with a curved surface is not a polyhedron.
Counting Faces, Edges, Vertices
- A prism has two identical parallel polygon bases joined by rectangular side faces.
- A pyramid has one polygon base, and triangular side faces that meet at a single top vertex (apex).
- For an n-sided base, use the rules below to count faces (F), vertices (V) and edges (E).
Common mistake: Forgetting to count both bases of a prism, or the base of a pyramid, when counting faces.
Euler's Formula for Polyhedra
- For every convex polyhedron, faces plus vertices minus edges always equals two.
- If you know any two of F, V and E, you can find the third.
- Match the counts with the prism or pyramid rules to identify the solid.
Common mistake: Writing F + E - V = 2. Edges are subtracted, not vertices.
Regular Polyhedra
- In a regular polyhedron, all faces are identical regular polygons.
- The same number of faces meets at every vertex.
- A cube and a regular tetrahedron are examples. A cuboid with unequal sides is not regular.
Common mistake: Thinking equal faces are enough. The same number of faces must also meet at every vertex.
Cylinder and Cone Basics
- A cylinder has two circular bases joined by a curved surface. A cone has one circular base and a vertex.
- Lateral (curved) surface area covers only the curved part, not the circular bases.
- Here r is the radius, h is the height and l is the slant height of the cone.
Common mistake: Forgetting the one-third in the cone's volume, or using slant height l instead of height h.
Exam tips
- Identify the base polygon first, then apply the prism or pyramid counting rules.
- Check every answer for F, V and E with Euler's formula.
- If a solid has any curved surface, rule it out as a polyhedron.
Beta: made with AI and checked by a second AI. A teacher has not reviewed it yet.
Sample questions
What is a three-dimensional figure?
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Answer: C. A shape with length, width, and height
A three-dimensional figure is a geometric shape that has three dimensions: length, width, and height.
Which shape is not considered a polyhedron?
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Answer: C. Sphere
A polyhedron is a solid shape with flat polygonal faces, straight edges, and vertices. A sphere has no flat faces, so it is not a polyhedron.
What distinguishes a regular polyhedron from other polyhedra?
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Answer: B. All its faces are regular polygons
A regular polyhedron is a three-dimensional solid where all the faces are regular, congruent polygons arranged symmetrically.
Can you determine the shape if it has 12 edges, 6 faces, and 8 vertices?
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Answer: A. Cuboid
A cuboid, or rectangular prism, has 12 edges, 6 faces (each a rectangle), and 8 vertices.
What is the formula for the volume of a cone?
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Answer: A. 1/3 x π x r^2 x h
The volume of a cone is given by one-third of the base area (πr^2) times the height (h), or V = 1/3 x π x r^2 x h.
More questions in this quiz
Answers and explanations are in the full quiz.
- Which of the following is a three-dimensional figure?
- Which three-dimensional figure has a circular base and a vertex?
- Which three-dimensional figure does not have curved surfaces?
- What is the shape of a cylinder's base?
- Which of the following has a maximum number of edges among the given shapes?
- A solid has 6 vertices and 9 edges. What is this solid figure?
- Find the number of faces in a prism that has a hexagonal base.
- How is the lateral area of a cylinder determined?
- In a pyramid, how do you determine the number of edges?
- How many diagonal edges does a regular tetrahedron have?
- A shape has 15 edges and 10 vertices. Which shape could it be?
- How many faces does a polyhedron have if it follows Euler's formula with 20 edges and 12 vertices?
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