1. Use Euler's Formula to find the missing number. edges:49

Faces:21

Vertices:?

A. 30

B. 32

C. 26

D. 28

2. What is the scale factor of a cube with a volume of 512m^3 to a cube with a volume of 3,375 m*3?

A. 8:15

B. 64:225

C. 15:8

D. 225:64

Question 1:

By definition, euler's formula is given by:

C + V = A + 2

Where,

C: number of faces

V: number of vertices

A: number of edges

Substituting values we have:

21 + V = 49 + 2

Clearing V we have:

V = 49 + 2-21

V = 30

Answer:

the missing number is:

A. 30

Question 2:

The volume of the cube is:

V1 = L1 ^ 3 = 512

The volume of the new cube is:

V2 = L2 ^ 3 = 3375

V2 = (kL1) ^ 3 = 3375

V2 = k ^ 3 (L1) ^ 3 = 3375

V2 = k ^ 3V1 = 3375

Therefore, the scale factor will be:

k ^ 3 = V1 / V2

k ^ 3 = 512/3375

k = (512/3375) ^ (1/3)

k = 8/15

Answer:

the scale factor of a cube with a volume of 512m ^ 3 to a cube with a volume of 3,375 m * 3 is:

A. 8:15