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Consider an incomplete pyramid of balls on a square base having 18 layers and having 13 balls on each side of the top layer then the total number N of balls in that pyramid satifies- (a) 900010000 (b) 80009000 (c) 70008000 (d) 1000012000

Consider an incomplete pyramid of balls on a square base having 18 layers and having 13 balls on each side of the top layer then the total number N of balls in that pyramid satifies-
(a) 900010000
(b) 80009000
(c) 70008000
(d) 1000012000
 

Grade:10

2 Answers

BALAJI ANDALAMALA
askIITians Faculty 78 Points
8 years ago
Top layer has 13*13 balls.
Similarly one layer below the top layer will have 14*14 balls.

We have 18 layers. So

N = 13^2+14^2+15^2+........+30^2
N=\frac{30\times31\times 61}{6}-\frac{12\times13 \times 25 }{6}
N=8805
Govind
14 Points
5 years ago
sum of squares of no. ranging from 18 to30 = sum of square of 30no.s -square of 12 no.s.Apply th formula n(n+1)2n+1)/6substitute 30 and 12 as n and subtract to get 8805

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