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Consider an incomplete pyramid of balls ...

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 satisfies

A

`9000 lt N lt 10000`

B

`8000 lt N lt 9000`

C

`7000 lt N lt 8000`

D

`10000 lt N lt 12000`

Text Solution

Verified by Experts

The correct Answer is:
B
Top layer has `(13 xx 13)` balls similarly are layer below top layer will have `(14 xx 14)` balls
We have 18 layer
So total number of balls
`N=(13)^(2)+(14)^(2)+……..+(30)^(2)`
`N = (30xx31xx61)/6-(12xx13xx25)/6`
`N= 8805`.
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