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
 
 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
 
 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

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