There are 8436 steel balls, each with radius of 1 centimeter, stacked in pile, with 1 ball on top, 3 balls in the second layer, 6 in the third layer 10 in the fourth and so on. The number of horizontal layers in the pile is
Explanation
Correct Option - 3
Given
Total steel Balls: 8436
Calculations:
Balls stacked in pile
According to question,
For any layer, the starting number, a =1
Difference, d= 2–1 = 3–2 = 4–3 = 1
Sn = (n/2)(2 + (n-1)) —(1)
A table can be made as follows based on equation. (1).
Cumulative sum = Sum of balls stacked upto (n-1) th layer + Sum of balls in n th lay
Balls in first layer + Summision of remaining laters = 8436
After stacking layer 36, we find that 8436 balls are utilized.
