Visualising Solid Shapes quiz

The number of faces of a cube is:

Euler's formula for polyhedrons is:

Which of the following is not a polyhedron?

The number of vertices of a triangular pyramid is:

The top view of a cylinder standing on its base is a:

The number of edges of a triangular prism is:

The lateral faces of a pyramid are:

A polyhedron has 6 faces and 8 vertices. Its number of edges is:

The front view of a cone standing on its base is a:

The regular polyhedron with four faces, each an equilateral triangle, is a:

Distinguish between a prism and a pyramid with respect to their bases and lateral faces. (2 marks)

Can a polyhedron have only 3 faces? Give a reason. (2 marks)

Name the solid whose net consists of two circles and a rectangle. Draw a rough sketch of the net. (2 marks)

Write the number of faces, vertices and edges of a pentagonal prism. (2 marks)

What is meant by the top view of a solid? Draw the top view of a cone standing on its base. (2 marks)

Is a square prism the same as a cuboid? Explain. (2 marks)

Give two reasons why a map is different from a picture. (2 marks)

Name the regular polyhedron with 8 faces, each an equilateral triangle. How many vertices does it have? (2 marks)

A pyramid has 10 edges. What is the shape of its base and how many faces does it have? (2 marks)

Why is a cuboid with unequal edges a convex polyhedron but not a regular polyhedron? (2 marks)

A prism whose base has n sides has n + 2 faces, 2n vertices and 3n edges. Find these numbers for an octagonal prism and verify Euler's formula. (3 marks)

(i) A polyhedron has 12 vertices and 30 edges. How many faces does it have? (ii) A polyhedron has 9 faces and 16 edges. Find the number of vertices and name a polyhedron with these numbers. (3 marks)

On a map with scale 1 cm represents 2.5 km, two villages are 6.4 cm apart. Find the actual distance. How long will a bus moving at 40 km/h take to travel between them along a straight road? (3 marks)

A staircase is built from unit cubes with 4 steps, the bottom step being 4 cubes long, the next 3, then 2, then 1, and the staircase is one cube wide. How many cubes are used? How many would be used if the staircase were 3 cubes wide? (3 marks)

A wooden cube of edge 3 cm is painted on all its faces and then cut into 27 cubes of edge 1 cm. How many small cubes have paint on exactly 3 faces, 2 faces, 1 face and no face? (3 marks)

Read the passage and answer the questions. A gift shop sells chocolates in boxes shaped like hexagonal prisms. Each box has two regular hexagonal faces joined by rectangular faces. (i) Find the number of faces, vertices and edges of the box. (ii) Verify Euler's formula for the box. (iii) Describe the net of the box. (5 marks)

Read the passage and answer the questions. The Great Pyramid of Giza has a square base and four triangular faces that meet at a single point at the top. (i) Find the number of faces, vertices and edges of a square pyramid. (ii) Draw the front view and the top view of a square pyramid. (iii) Verify Euler's formula for the square pyramid. (5 marks)

Read the passage and answer the questions. Rina drew a map of her area using the scale 1 cm represents 200 m. On her map, the school is 3 cm east of her home and the market is 4 cm north of the school. (i) Find the actual distance from her home to the school. (ii) Find the actual distance from the school to the market. (iii) Find the straight-line distance from her home to the market. (5 marks)

Read the passage and answer the questions. An ordinary die is a cube with the numbers 1 to 6 on its faces, arranged so that the numbers on opposite faces always add up to 7. (i) Which number is opposite the face showing 2? (ii) What is the total of the numbers on all the faces? (iii) Can you see the faces showing 1 and 6 at the same time? Explain. (5 marks)

Read the passage and answer the questions. A classic football is made of 12 regular pentagons and 20 regular hexagons stitched together, so that every corner is shared by three patches. (i) How many faces does this shape have? (ii) Each edge is shared by two patches. Find the number of edges. (iii) Use Euler's formula to find the number of vertices, and check your answer using the fact that three patches meet at each vertex. (5 marks)

A model house is made of a cuboid with a triangular prism as its roof. Draw a sketch of the model and its front view, side view and top view. Count the faces, vertices and edges of the combined solid and verify Euler's formula. (6 marks)

Draw the nets of a cube, a cuboid, a square pyramid, a triangular prism, a cylinder and a cone, and label each net with the name of the solid it forms. (6 marks)

Explain Euler's formula and verify it for a cube, a tetrahedron and an octagonal pyramid. Find the faces, vertices and edges of a pentagonal pyramid and a pentagonal prism. Explain why Euler's formula is not used for a cylinder or a cone. (6 marks)

On isometric dot paper, sketch (i) a cuboid of dimensions 3 by 2 by 2 units (ii) an L-shaped solid made of 4 unit cubes. Draw the top view and the front view of the L-shaped solid and state how many unit cubes the cuboid contains. (6 marks)

From her home, Meena walks 500 m east to a bus stop and then 1.2 km north to her school. Draw a map of the route using the scale 1 cm represents 100 m, marking the home, bus stop and school with suitable symbols. Find the straight-line distance between her home and the school, and explain how a map differs from a picture of the same area. (6 marks)