Can a polyhedron have 10 faces, 20 edges and 15 vertices? Justify you answer. [4 MARKS]

Open in App

Solution

Formula :1 Mark
Answer : 1 Mark
Reason : 2 Marks

By Euler's formula,

F + V - E = 2

Substituing the given values

$\Rightarrow 10 + 15 - 20 = 35 - 20 = 15 \neq 2$

Any solid to be called as polyhedron need to satisfy the Euler's formula.

$\Rightarrow$ A polyhedron can not have 10 faces, 20 edges and 15 vertices.

Suggest Corrections

Similar questions

Q. Question 8
Can a polyhedron have 10 faces, 20 edges and 15 vertices?

Q. Question 8
Can a polyhedron have 10 faces, 20 edges and 15 vertices?

Q. (a) Can a polyhedron have 10 faces, 20 edges and 15 vertices? Justify your answer.

(b) A glowing bulb is kept above the following solids. Name the shape of the shadows obtained in each case. Attempt to give a rough sketch of the shadow.

[4 MARKS]

Q. Question 49

State whether the following statement is True or False.

A polyhedron can have 10 faces, 20 edges and 15 vertices.

(a) Can a polyhedron have 10 faces, 20 edges and 15 vertices? Justify your answer.

(b) A glowing bulb is kept above the following solids. Name the shape of the shadows obtained in each case. Attempt to give a rough sketch of the shadow.

[4 MARKS]

Join BYJU'S Learning Program

Can a polyhedron have 10 faces, 20 edges and 15 vertices? Justify you answer. [4 MARKS]

Formula :1 Mark Answer : 1 Mark Reason : 2 Marks By Euler's formula, F + V - E = 2 Substituing the given values ⇒10+15−20=35−20=15≠2 Any solid to be called as polyhedron need to satisfy the Euler's formula. ⇒ A polyhedron can not have 10 faces, 20 edges and 15 vertices.