Question

A polyhedron has 5 faces and 8 edges. What is the number of vertices of the polyhedron?

5

11

8

13

Answer 1

13

Answer 2

can yu explain please

Answer 3

You need to use Eulers formula

Answer 4

can sum one walk me through it please

Answer 5

see here: http://www.wolframalpha.com/input/?i=eulers+equation&a=*C.eulers+equation-_*FamousMathProblems.dflt-&a=*DPClash.FamousMathProblemsE.eulers+equation-_*PolyhedralTheorem-

Answer 6

the answer is 5 thats what i got bc

V+F-E=2
V+8-5=2
8-5+2=V
3+2=V
5=V

Answer 7

you have the faces/edges reversed

Answer 8

oh . ok

so its
V+5-8=2
5-8+2=V
-3+2=V
-1=V

Answer 9

im confused nw can i please get a explanation

Answer 10

V + 5 - 8 = 2
V - 3 = 2 <--- (5 - 8 = -3)
V = 2 + 3 <--- (add 3 to both sides)

Answer 11

im still a little lost

Answer 12

where abouts?

Answer 13

is it the algebra that is confusing you?

Answer 14

sorta yes bc im in geometry and i dnt really remember the alegra parts anymore

Answer 15

ok, lets do this one step at a time...

Answer 16

ok

Answer 17

Eulers formula tells us that for a convex polyhedron, we have:

V + F - E = 2

where:
V = number of vertices
F = number of faces = 5 (in this case)
E = number of edges = 8 (in this case)

Answer 18

ok so far?

Answer 19

yess

Answer 20

ok, what we need to find is the number of vertices V, so we could first re-arrange the equation as follows:

V + F - E = 2
V + F - E + E = 2 + E (adding E to both sides)
V + F = 2 + E (since -E + E cancel each other out)
V + F - F = 2 + E - F (subtracting F from both sides)
V = 2 + E - F (since F - F cancel each other out)

ok so far?

Answer 21

yes

Answer 22

ok, good, so we have ended up with:

V = 2 + E - F

now lets plug in the values E=8, F=5 to get:

V = 2 + 8 - 5
= 10 - 5
= 5

Answer 23

hopefully it all makes more sense now?

Answer 24

yes very much thank yuu soo much .

Answer 25

yw - I'm glad I was able to help :)