Question

Consider an incomplete pyramid of balls on a square base having $18$ players, and having $13$ balls on each side of the top layer. Then the total number $N$ of balls in that pyramid satisfies

• A. $9000<N<10000$
• B. $8000<N<9000$
• C. $7000<N<8000$
• D. $10000<N<12000$

Answer 1

Answer: (B)

$8000<N<9000$

Top layer has $(13\times 13)$ balls
Similarly one layer below top layer will have $(14\times 14)$ balls and we have $18$ lesens to total number of ball
$N=(13{)}^2+(14{)}^2+....+(30{)}^2$
$N=\frac{30\times 31\times 61}{6}=\frac{12\times 13\times 25}{6}$
$N=8805$