8. Can a polyhedron have 10 faces, 20 edges and 15 vertices?
7. Using Euler’s formula find the unknown.
6. Verify Euler’s formula for these solids.
6. Verify Euler’s formula for these solids.
5. Is a square prism same as a cube? Explain.
4. (i) How are prisms and cylinders alike?
3. Which are prisms among the following?
3. Which are prisms among the following?
3. Which are prisms among the following?
3. Which are prisms among the following?
2. Is it possible to have a polyhedron with any given number of faces? (Hint: Think of a pyramid).
1. Can a polyhedron have for its faces
(iii) a square and four triangles?
1. Can a polyhedron have for its faces
(ii) 4 triangles?
1. Can a polyhedron have for its faces
(i) 3 triangles?
Tabulate the number of faces, edges and vertices for the following polyhedrons: (Here ‘V’ stands for number of vertices, ‘F’ stands for number of faces and ‘E’ stands for number of edges).
Solid | F | V | E | F+V | E+2 |
---|---|---|---|---|---|
Cuboid | |||||
Triangular pyramid | |||||
Triangular prism | |||||
Pyramid with square base | |||||
Prism with square base |
What do you infer from the last two columns? In each case, do you find
, i.e., ? This relationship is called Euler’s formula.
In fact this formula is true for any polyhedron.
4. Draw a map giving instructions to your friend so that she reaches your house without any difficulty.
3. Draw a map of your school compound using proper scale and symbols for various features like play ground main building, garden etc.
2. Draw a map of your class room using proper scale and symbols for different objects.
1. Look at the given map of a city.
Answer the following.
(e) Which is further south, the primary school or the Sr. Secondary School?
1. Look at the given map of a city.
Answer the following.
(d) Which is further east, the city park or the market?