Q17 of 42 Page 10

Can a polyhedron have 10 faces, 20 edges and 15 vertices?

Number of faces = F = 10

Number of edges = E = 20


Number of vertices = V = 15


Any polyhedron satisfies Euler's Formula, according to which, F + V - E = 2


For the given polygon,


F + V - E = 10 + 15 - 20


= 25 - 20


= 5 ≠ 2


Since Euler's formula is not satisfied, such a polyhedron is not possible

More from this chapter

All 42 →
15

The actual length of a painting was 2 m. What is its length in the photograph if the scale used is 1 mm : 20 cm.

 16

Look at the map given below :


Now answer the following questions.


(a) Name the roads that meet at round about.


(b) What is the address of the stadium?


(c) On which road is the Police Station situated?


(d) If Ritika stays adjacent to bank and you have to send her a card. What address will you write?


(e) Which sector has maximum number of houses?


(f) In which sector is Fire Station located?


(g) In the map, how many sectors have been shown?

 18

Identify the nets given below and mention the name of the corresponding solid in the space provided.

 19

The side of a square board is 50 cm. A student has to draw its image in her notebook. If the drawing of the square board in the notebook has perimeter of 40 cm, then by which scale the figure has been drawn?