Question

You a Miguel Cervantes de Navas y Colon, captain in the Royal Spanish Army in Seville in the year 1842. Outside your barracks window is a stack of cannonballs, as shown in the illustration. On an idle afternoon you decide to calculate the number of cannonballs in the stack. what is the number of cannonballs.

Answer 1

650 cannonballs

Explanation step by step:

upper layer = 1 ^ 2

second layer = 2 ^ 2

third layer = 3 ^ 2

layer 12 is 12 ^ 2

The formula is:

n * (n + 1) * (2n + 1) / 6

n = 12

12 (12 + 1) (2 * 12 + 1) / 6

12 * 13 * 25/6 =

650

There are 650 cannonballs in this pyramid.

Answer 2

650 cannonballs

A

Explanation:

The stack of Cannonballs is really the sum of squares.

The top layer is 1^2

The second layer is 2^2

The Third layer is 3^2

....

layer 12 ( the bottom layer) is 12^2

The formula for this is

n*(n + 1)*(2n + 1)/6

n = 12

12(12 + 1)(2*12 + 1)/6

12 * 13 * 25/6

650

The sum of this pyramid is 650 Cannonballs