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Solid Shapes Quiz - CBSE Class 6 Mathematics

Free practice quiz: Solid Shapes (CBSE Class 6 Mathematics). 15 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This CBSE Class 6 Mathematics practice quiz has 15 multiple-choice questions on Solid Shapes, and 15 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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Solid shapes and their parts

  • A solid shape takes up space and has length, breadth and height, like a box or ball.
  • Flat shapes such as a square, circle or triangle are not solids; they lie flat on paper.
  • Faces are flat surfaces, edges are where two faces meet, and vertices are corner points.
Prism with n-sided base
\[F = n + 2,\ E = 3n,\ V = 2n\]
Pyramid with n-sided base
\[F = n + 1,\ E = 2n,\ V = n + 1\]

Common mistake: Counting only the faces you can see in a drawing and forgetting the hidden faces, edges and vertices at the back.

Euler's formula for polyhedra

  • A polyhedron is a solid with only flat polygon faces, straight edges and corner vertices.
  • For every such solid, faces plus vertices is always two more than the number of edges.
Euler's formula
\[F + V - E = 2\]
Finding edges
\[E = F + V - 2\]

Common mistake: Using Euler's formula for cylinders, cones or spheres. They have curved surfaces, so they are not polyhedra.

Solids with curved surfaces

  • A cylinder has two circular faces and one curved surface. A cone has one circular base and a pointed vertex.
  • A sphere is a perfectly round ball with only one curved surface and no edges or vertices.
  • Rotating a rectangle about a side makes a cylinder. Rotating a right triangle about a shorter side makes a cone.

Common mistake: Thinking a cone has no flat face. Its base is a flat circle. Only its side is curved.

Volume of prisms and cylinders

  • Volume is the space a solid fills, measured in cubic units like cm³.
  • For any prism or cylinder, multiply the area of the base by the height.
  • To find a missing side of a cuboid, divide the volume by the product of the other two sides.
Cuboid
\[V = l \times b \times h\]
Cube
\[V = a^3\]
Any prism
\[V = \text{Base area} \times h\]
Cylinder
\[V = \pi r^2 h\]

Common mistake: Using the diameter instead of the radius in the cylinder formula, or forgetting to square the radius.

Surface area of a sphere

  • Surface area is the total area covering the outside of a solid, measured in square units like cm².
  • A sphere's surface area depends only on its radius.
Sphere surface area
\[A = 4\pi r^2\]

Common mistake: Cubing the radius instead of squaring it. Cubing belongs to volume, not surface area.

Exam tips

Beta: made with AI and checked by a second AI. A teacher has not reviewed it yet.

Sample questions

  1. What is a solid shape?

    Show answer

    Answer: B. A three-dimensional shape

    A solid shape is a three-dimensional shape that has volume and takes up space. Examples include cubes, spheres, and cylinders.

  2. What shape is formed when you rotate a rectangle about one of its sides?

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    Answer: B. Cylinder

    When a rectangle is rotated around one of its sides, it forms a cylindrical shape.

  3. Which solid shape has a circular base and a pointed top?

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    Answer: C. Cone

    A cone is recognized by its circular base that tapers smoothly to a point or apex.

  4. If a sphere has a radius of 3 cm, what is its surface area?

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    Answer: B. 36π cm²

    The surface area of a sphere can be calculated using the formula A = 4πr². For a sphere with a radius of 3 cm, A = 4π(3)² = 36π cm².

  5. What is the relationship of edges and faces in a polyhedron?

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    Answer: A. Faces + Edges = Vertices + 2

    This is a form of Euler's formula, which states that for any convex polyhedron, the relation is Faces + Edges = Vertices + 2.

Take the full quiz

More questions in this quiz

Answers and explanations are in the full quiz.

  1. Which of the following is NOT a solid shape?
  2. How many faces does a cube have?
  3. Which of the following has a curved surface?
  4. How many edges does a triangular prism have?
  5. A rectangular prism has a length of 4 cm, width of 3 cm, and height of 5 cm. What is its volume?
  6. How many vertices does a square pyramid have?
  7. Calculate the volume of a cylinder with a height of 7 cm and a radius of 2 cm.
  8. A hexagonal prism has a height of 10 cm. If the area of its base is 30 cm², what is its volume?
  9. A rectangular prism and a cube have the same volume. If the cube has a side length of 4 cm, what could be the possible dimensions of the rectangular prism?
  10. If a box has a volume of 120 cm³ and its dimensions are 2 cm in height and 5 cm in width, what is the length of the box?

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