Question

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

Answer 1

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