One side of the bottom layer of a triangular pyramid has 12 balls. How many are there in the whole pyramid?Note that the pyramid is equilateral and solid.
Choose the correct choice from the following answers
A) 286  B) 364  C) 504  D) 164  E) 165

Rationale: as there are 12 balls along one side , it means that there are 12 layers of balls . the top most layer has 1 ball . the second layer has 3 ( 1 + 2 ) balls . the third layer has 6 ( 1 + 2 + 3 ) balls . the fourth layer has 10 ( 1 + 2 + 3 + 4 ) balls . the fifth layer has 15 ( 1 + 2 + 3 + 4 + 5 ) balls . similarly , there are 21 , 28 , 36 , 45 , 55 , 66 and 78 balls in the remaining layers . hence , the total number of balls are = 1 + 3 + 6 + 10 + 15 + 21 + 28 + 36 + 45 + 55 + 66 + 78 = 364 balls answer : b
Answer: B